Problems on Trains -

Discussion

1. km/hr to m/s
conversion:

a km/hr = a x 5
m/s. 18

2. m/s to km/hr
conversion:

a m/s = a x 18
km/hr. 5

3. Formulas for finding Speed, Time and Distance 4. Time taken by a train of
length l metres to pass a pole or standing man or a signal post is
equal to the time taken by the train to cover l metres. 5. Time taken by a train
of length l metres to pass a stationery object of length b metres is
the time taken by the train to cover (l + b) metres. 6. Suppose two trains or two
objects bodies are moving in the same direction at u m/s and v
m/s, where u > v, then their relative speed is = (u - v) m/s. 7. Suppose two trains
or two objects bodies are moving in opposite directions at u m/s and v
m/s, then their relative speed is = (u + v) m/s. 8. If two trains of length a metres
and b metres are moving in opposite directions at u m/s
and v m/s,
then:

The time taken by the trains to cross each other =

(a + b) sec.
(u + v)

9. If two trains of length a metres and b metres are moving in the same
direction at u m/s
and v m/s,
then:

The time taken by the faster train to cross the slower train =
(a + b) sec.
(u - v)

10. If two trains (or bodies) start at the same time from points A and B towards
each other
and after crossing they take a and b sec in reaching B and A
respectively, then:
 (A's speed) : (B's speed) =
(b : a)
1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the
length of the train? [A]. 120 metres [B]. 180 metres [C]. 324 metres [D]. 150 metres
Answer: Option D
Explanation:
Speed= 60 x 18 5
m/sec = 50 3 m/sec. Length of the train = (Speed x
Time) =
50 x 3
9 m = 150 m. Distance = Time *speed 1km =1000Meteres 1hr =3600 seconds Distance =
60*9/3600 =9/60 km Distane in Metres =(9/60)*1000 =150M simple and fast way
Distance = time*speed. Distance = 9sec*60(km/hr).
Here the the time is in 'seconds' and answer will given into the 'm', so we will convert all the
values into the 'm&sec'.
1km = 1000m. 1hr = 3600sec.
Then, Distance = 9*60(1000/3600). Distance = 9*60(5/18). Distance = 150m.
2. A train 125 m long passes a man, running at 5
km/hr in the same direction in which the train is going, in 10 seconds. The speed of
the train is:
[A]. 45 km/hr [B]. 50 km/hr [C]. 54 km/hr [D]. 55 km/hr
Answer: Option B
Explanation:
Speed of the train relative to man = 125
m/sec 10 = 25
m/sec. 2 = 25 x 18
km/hr 2 5
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 x = 50 km/hr. Or Distance = time * speed 125 = 10 * speed distance/time =
speed 125/10 = (25/2)m/s = speed ---------------------------------------------------------- Answer
should be in km/hr so convert m/s km = 1000m and hr = 3600s m = km/1000 and s =
hr/3600 m/s = (3600/1000)km/hr m/s = (18/5)km/hr ------------------------------------------------------
---- The condition was speed = (25/2)m/s = (25/2)(18/5)km/hr = 45 km/hr The speed was
relative to man so we have taken time in consideration of man ----------------------------------------
---------------- See further in in view answer. ----------------------------------------------------------
3. The length of the bridge, which a train 130
metres long and travelling at 45 km/hr can cross in 30 seconds, is: [A]. 200 m [B].
225 m [C]. 245 m [D]. 250 m
Answer: Option C
Explanation:
Speed = 45 x 5
m/sec = 25 m/sec. 18 2
Time = 30 sec.
Let the length of bridge be x metres.
Then, 130 + x = 25 30 2
2(130 + x) = 750
x = 245 m.
Length of the train= 130. Speed of the train = 45km/hr. time=30sec. lengthof bridge =
x+length of train. x+length of train = Speed of the train *time. x+130=45*5/18*30. x+130
=375 x=375-130 x=245
4. Two trains running in opposite directions cross a man standing on the platform in
27 seconds and 17 seconds respectively and they cross each other in 23 seconds.
The ratio of their speeds is: [A]. 1 : 3 [B]. 3 : 2 [C]. 3 : 4 [D]. None of these
Answer: Option B
Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
27x + 17y = 23 x+ y
27x + 17y = 23x + 23y
4x = 6y
x = 3 . y 2 27 17
23
23-17=6 27-23=4
Then ratio become 3:2
5. A train passes a station platform in 36 seconds
and a man standing on the platform in 20 seconds. If the speed of the train is 54
km/hr, what is the length of the platform? [A]. 120 m [B]. 240 m [C]. 300 m [D].
None of these
Answer: Option B
Explanation:
Speed = 54 x 5
m/sec = 15 m/sec. 18
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, x + 300 = 15 36
x + 300 = 540
x = 240 m. Or
In simple process,
Bs-------------------m------------Be
A--------20S---------B------16S---C
l---------------36s---------------l
If man was reference point then T.P=36-20=16s. We know length=speed*time. Then lenth of
train=(54*5/18)*16=15m/s.*16s.=240m.
Answer=240m.
6. A train 240 m long passes a pole in 24 seconds.
How long will it take to pass a platform 650 m long? [A]. 65 sec [B]. 89 sec [C]. 100
sec [D]. 150 sec
Answer: Option B
Explanation:
Speed = 240
m/sec = 10 m/sec. 24 Required time = 240 + 650
sec = 89 sec. 10
Or We can calculate the train speed by considering pole as a reference point train length=240m time taken by a
train to pass a pole =24sec s=d/t s=(240/24) s=10m/sec platform length=650m we know that
total distance=speed*time 650+240=10*t 890=10*t t=89sec
7. Two trains of equal length are running on
parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes
the slower
train in 36 seconds. The length of each train is: [A]. 50 m [B]. 72 m [C]. 80 m [D]. 82
m
Answer: Option A
Explanation:
Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
= 10 x 5
m/sec 18 = 25
m/sec 9 2x = 25 36 9
2x = 100
x = 50.
Or Length of the train =X m by converting it into km...........
(X/36)*(18/5)=X/10 KM
X/10 = 46-36 = 10
X=100 both are same length therefore 2X=100 ..... LENGTH OF BOTH TRAIN X=50........
LENGTH OF EACH TRAIN
8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a
bridge 140 m long? [A]. 40 sec [B]. 42 sec [C]. 45 sec [D]. 48 sec
Answer: Option A
Explanation:
Formula for converting from km/hr to m/s: X km/hr =
5 18 m/s. Therefore, Speed
=
5
m/sec = 25 18 2 m/sec. Total distance to be covered = (360 + 140) m = 500 m.
Formula for finding Time = Distance
Speed Required time = 500 x 2
25 sec = 40 sec. Or Convert 45km to m i.e. 45000m & 1hr=3600sec.
Then, 45000/3600sec. therefore 12.5m/sec. Total distance to be covered is 360m + 140m =
500m
Then, time required to pass the bridge is 500m/12.5m/s = 40sec.
9. Two trains are moving in opposite
directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km
respectively. The time taken by the slower train to cross the faster train in seconds
is: [A]. 36 [B]. 45 [C]. 48 [D]. 49
Answer: Option C
Explanation:
Relative speed = (60+ 90) km/hr
= 150 x 18
5 m/sec 45
x
Xx
= 125
m/sec. 3
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time = 2000 x 3
sec = 48 sec. 125 Or Length of the two trains=2km (the units I have taken is all in kms).
Relative speed is 150km/hr (this too in kms).
S=Length/Time=>time=length/speed.
Time=2/150=1/75 of a second i.e., 1/75*60 (converted into minutes) =4/5.
4/5*60 (into seconds) =48 sec.
10. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the
engine of a 120 metres long train running at 45 kmph in the same direction. In how
much time will the train pass the jogger? [A]. 3.6 sec [B]. 18 sec [C]. 36 sec [D]. 72
sec
Answer: Option C
Explanation:
Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.
= 36 x 5
m/sec 18
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.
Time taken = 360
sec = 36 sec.
Relative speed means speed of an object w.r.t to another object.
Tips:
1.)Two objects moving in same direction-->stop object 2 and subtract object 2' s speed from
object 1.
Ex: Suppose two cars moving in same direction with 60 kmph(both cars same speed)..it is
obvious that relative speed is 0 kmph....how did it come??? by subtracting..ok.
2.) Two objects moving in oppsite direction--->stop obj 2 and add its speed to obj1.
Ex: Car1 speed=40 kmph in east direction. Car2 speed=50 kmph in west direction. Relative
speed of car1 w.r.t car2 is stop car2, add its speed to car1, i.e 40+50 = 90.
11. A 270 metres long train running at the speed of 120 kmph crosses another train
running in
opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the
other train? [A]. 230 m [B]. 240 m [C]. 260 m [D]. 320 m [E]. None of these
Answer: Option A
Explanation:
Relative speed = (120 + 80) km/hr
= 200 x 5
m/sec 18 = 500
m/sec. 9
Let the length of the other train be x metres.
Then, x + 270 = 500
99
x + 270 = 500
x = 230. or As given: 120+80=200 200*5/18=500/9
Let the length of other train be X then X+270/9=500/9 cross multiply, u vl get 9X + 2430=
4500 9X=2070. .'. X=2070/9 x=230
12. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in
26 seconds.
What is the length of the goods train? [A]. 230 m [B]. 240 m [C]. 260 m [D]. 270 m
Answer: Option D
Explanation:
Speed = 72 x 5
m/sec = 20 m/sec. 18
Time = 26 sec.
Let the length of the train be x metres.
Then, x + 250 = 20 26
x + 250 = 520
x = 270. or 1 km = 1000 meters. 1 hr = 3600 seconds.
1 km/hr = 1000/3600 m/s
= 10/36 m/s
= 5/18 m/s.
Therefore 1 km/hr = 5/18 m/sec.
13. Two trains, each 100 m long, moving in opposite directions, cross each other in 8
seconds. If
one is moving twice as fast the other, then the speed of the faster train is: [A]. 30
km/hr [B]. 45 km/hr [C]. 60 km/hr [D]. 75 km/hr
Answer: Option C
Explanation:
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
(100 + 100) = 3x 8
24x = 200
x = 25 . 3 So, speed of the faster train = 50 m/sec 3
= 50 x 18
km/hr 3 5
= 60 km/hr. or 1) if 2 things moves in same direction: time they meet t=(x+y)/(u-v) where x,y-distance of
trains or smthng u,v-speed's in mps.
2) if 2 things moves in opposite direction: time they meet t=(x+y)/(u+v)
14. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr
respectively in
opposite directions on parallel tracks. The time (in seconds) which they take to cross
each other, is: [A]. 9 [B]. 9.6 [C]. 10 [D]. 10.8
Answer: Option D
Explanation:
Relative speed = (60 + 40) km/hr = 100 x 5
m/sec = 250 m/sec. 18 9
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = 300 x 9
sec = 54 sec = 10.8 sec. 250 5
or Convert km/h in m/sec.
In first we have 1 km = 1000 m.
In second we have 1 hour = 60 min.
And 1 min = 60 sec.
So total sec in 1 hrs = 60 x 60 = 3600 sec.
So 1000 m/3600 sec = 10/36 [cut 2 zero].
And finally divided by 2 both number.
So 5/18 m/s.
15. A train 110 metres long is running with a speed of 60 kmph. In what time will it
pass a man
who is running at 6 kmph in the direction opposite to that in which the train is going?
[A]. 5 sec [B]. 6 sec [C]. 7 sec [D]. 10 sec
Answer: Option B
Explanation:
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
= 66 x 5
m/sec 18 = 55
m/sec. 3 Time taken to pass the man = 110 x 3
sec = 6 sec. or speed=distance/time
time=distance/speed
speed = 66*5/18 [Converting km/hr to m/sec]
= 55/3 m/sec.
Therefore, time = 110/55*3
= 110*3/55
= 6 sec
16. A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile
long. How long does it take for the train to pass through the tunnel from the moment
the front enters to the moment the rear emerges? [A]. 2.5 min [B]. 3 min [C]. 3.2 min
[D]. 3.5 min

Answer:
Option B

Explana
tion:

Total distance covered = 7 + 1

miles 2 4
= 15 miles. 4
Time taken = 15 hrs 4 x
75
= 1 hrs 1
20 = x 60 min. 20 = 3
min. or Answer is 3 min because.

Given is speed = 75 miles

per hour Total distance is
7/2 + 1/4 = 15/4

Distance is 15/4 because in question it is mentioned that calculate time from entry
of tunnel to the point when train's rear left the tunnel.
7/2 miles 1/4 miles

<---------------------------------><------->

_________________________________ train

entry of [ tunnel ]__________

tunnel [_________________________________]__________]--> -->

17. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel
in 1 minute,
then the length of the tunnel (in meters) is:
[A]. 130 [B]. 360 [C]. 500 [D]. 540

Answer:
Option C
 Explana
tion:

Speed = 78 x 5 m/sec = 65
m/sec.
18 3

Time = 1 minute = 60
seconds.

Let the length of the tunnel be x

metres.

Then, 800 + x =
65 60 3

3(800 + x) =
3900

x=
500
.

or Length of the tunnel = x length of the train = 800 relatively (x+800) ----------------------- train
crosses the platform 78 km/hr , we have to convert km/hr to m/s so the formula is
5/18 i.e., 78*(5/18)=65/3.

formula for calculatind the

distance is DISTANCE=
SPEED*TIME

TIME is given as 1min

i.e., 60 sec SPEED =65/3

distance =
65/3 * 60
distance =
1300

relative length (x+800)

= 1300 x = 1300- 800
therefore x= 500

18. A 300 metre long train crosses a platform in 39 seconds while it crosses a
signal pole in 18
 seconds. What is the length of the platform? [A]. 320 m
[B]. 350 m [C]. 650 m [D]. Data inadequate

Answer:
Option B
Explana
tion:

Speed = 300 m/sec = 50

m/sec. 18 3

Let the length of the platform be x

metres.

Then, x + 300 =
50 39 3

3(x + 300) =
1950

x = 350 m. or First, calculate a

speed of the train.

Length = Speed *
Time.

Then, S
= L/T.

300/18 = 16.66
m/s.

Then, L =
S * T.

(x + 300) =
16.66 * 39.

X=
350
m.

19. A train speeds past a pole in 15 seconds and a platform 100 m long in 25
seconds. Its length
is: [A]. 50 m [B]. 150 m [C]. 200 m [D]. Data inadequate
 Answer:
Option B

Explana
tion:

Let the length of the train be x metres and its speed

by y m/sec.

Then, x = 15 y = x . y
15
x+
100 =
x
25
15

15(x + 100)
= 25x

15x + 1500
= 25x

1500 =
10x

x = 150 m. or Let train's

length be x meters,

Then, train speed=train length/the time taken to cross

the poll.

=
x/
15
.

Train speed=total distance/the time to cross the

platform,

x/15 =
(x+100)/25.

x=
15
0.
20. A train moves past a telegraph post and a bridge 264 m long in 8 seconds
and 20 seconds
respectively. What is the speed of the train? [A].
69.5 km/hr [B]. 70 km/hr [C]. 79 km/hr [D]. 79.2
km/hr

Answer:
Option D

Explana
tion:

Let the length of the train be x metres and its speed

by y m/sec.

Then, x = 8 x = 8y y
Now, x + 264 = y 20

8y + 264
= 20y

y=
22
.

Speed = 22 m/sec = 22 x 18 km/hr = 79.2

km/hr. 5

or 1) Train cross the pole in 8 sec.

Speed =
Distance/Time.

Assume the train speed is x and length of

train be y.

x = y/8 or y
= 8x.

2) Train cross the bride which is 264mts

long 20 sec.

x=
(264+y)/2
0.
20x = 264+8x because y = 8x
in above.

Solving the above equation we get speed is

22m/sec.

Finally convert the m/sec to

km/hr.

22*18/5 = 79.2
km/hr.

21. How many seconds will a 500 metre long train take to cross a man walking with
a speed of 3
km/hr in the direction of the moving train if the speed of the train is
63 km/hr? [A]. 25 [B]. 30 [C]. 40 [D]. 45

Answer:
Option B

Explana
tion:

Speed of the train relative to man = (63 -

3) km/hr
= 60 km/hr = 60 x 5 m/sec 18 = 50 m/sec.
3
3 Time taken to pass the man = 500 x
sec 50
= 30
sec.

or Speed of train in m/s = 17.5.

Time taken to cross a

man = x.

Speed of man in m/s =

0.833.

17.5*x = 500 +
0.833*x. 16.66 x
= 500.
x=
30.00se
c.

22. Two goods train each 500 m long, are running in opposite directions on parallel
tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by
the slower train to pass the driver of the faster one. [A]. 12 sec [B]. 24 sec [C]. 48
sec [D]. 60 sec

Answer:
Option B

Explana
tion:

Relative speed = = (45 +

30) km/hr = 75 x 5 m/sec 18
= 125 m/sec. 6

We have to find the time taken by the slower train to pass the DRIVER of the
faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
Required time = 500 x 6 = 24 sec.
or d = s/t.
(500+500) = distance = 1000. Speed = 45kmph+30kmph = 75kmph.
Then convert it in to metre = 75*5/18 = 20.833333. t = d/s = 1000/20.83333 = 48sec.
Then 2x(two train) = 48sec ; x = 48/2 => x = 24sec for each train.
23. Two trains are running in opposite directions with the same speed. If the length
of each train
is 120 metres and they cross each other in 12 seconds, then the speed of each train
(in km/hr) is: [A]. 10 [B]. 18 [C]. 36 [D]. 72
Answer: Option C
Explanation:
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)
12
2x = 20
x = 10.
Speed of each train = 10 m/sec = 10 x 18 km/hr = 36 km/hr. 5
or Speed = distance/time.

Here, distance = 120 m i.e., 0.12 km; time = 12 sec i.e.,

12/60 x 60 hrs.

Hence, speed = 0.12/ (12/3600) = (0.12*3600) /12 =

36 km/hr.
24. Two trains of equal lengths take 10 seconds and 15 seconds respectively to
cross a telegraph post. If the length of each train be 120 metres, in what time (in
seconds) will they cross each other travelling in opposite direction? [A]. 10 [B]. 12
[C]. 15 [D]. 20

Answer:
Option B

Explana
tion:

Speed of the first train = 120 m/sec = 12

m/sec. 10 Speed of the second train = 120
m/sec = 8 m/sec. 15

Relative speed = (12 + 8) = 20

m/sec.

Required time = (120 + 120) sec = 12

sec.

or Length of each train is X.

Speed of 1st train is V1 =

X/10 m/s.

Speed of 2nd train is V2 =

X/15 m/s.

Relative speed is =
V1+V2.

Total distance they have to

cover is 2X.
Speed = (distance)
/time.

Distance = speed *
time.

Answer. (X/10) + (X/15) = 2X

* time.

time =
12sec.
As per given problem we can say time taken is independent on length of trains it's depend
only speed of train only.

25. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long
coming from
opposite direction in 6 seconds. The speed of the
second train is: [A]. 48 km/hr [B]. 54 km/hr [C]. 66
km/hr [D]. 82 km/hr

Answer:
Option D

Explana
tion:

Let the speed of the second train be

x km/hr.

Relative speed = (x +
50) km/hr
= (x + 50) x 5
m/sec 18 = 250 + 5x
m/sec. 18

Distance covered = (108 + 112) =

220 m.

220 = 6
250 +
5x
1
8

250 + 5x
= 660

x = 82
km/hr. or Solution
for 220
__________ =6
is (250+5x/18)
220*18 _______ =6 =>
220*18=6(250+5x) 250+5x
=> 220*3=(250+5x)
=>660=250+5x => 660-
250=5x =>410=5x =>x=82
or S =
D/T.

So, D = 108+112 =
220 m.

= 220/1000
km/hr.

T = 6 sec = 6/3600 =
1/600 hr.

S = 50
km/hr.

We assume second train

speed 'x'.

Relative speed = 50 km/hr+x

km/hr.

S=
D/T.

= 50+x =
220/1000*600.

= 50+x = 22*6 = 50+x =

132.

x = 82
km/hr.
26. Two trains are running at 40 km/hr and 20 km/hr respectively in the same
direction. Fast
train completely passes a man sitting in the slower train in 5 seconds. What is
the length of the fast train? [A]. 23 m [B]. 23 2 m 9 [C]. 27 7 m 9 [D]. 29 m

Answer:
Option C

Explana
tion:

Relative speed = (40 - 20) km/hr = 20 x 5 m/sec = 50

m/sec. 18 9
Length of faster train = 50 x 5 m = 250 m =
27 7 m. 9 9 9

or 1)First calculate the relative speed of two trains ( as they are moving in same direction it will be difference of two
train speeds).

Relative speed = 40-20 = 20 km/hr = 20*5/18

=50/9 m/s

2)Now faster crosses the man sitting in the slower one (irrespective of the position of
man it may be starting,middle or last) now use the formula

length of train (faster) = speed X time = 50/9*5 =

27 7/9 m

27. A train overtakes two persons who are walking in the same direction in which
the train is going, at the rate of 2 kmph and 4 kmph and passes them completely
in 9 and 10 seconds respectively. The length of the train is: [A]. 45 m [B]. 50 m
[C]. 54 m [D]. 72 m
Answer: Option B
Explanation:
2 kmph = 2 x 18 5 m/sec = 5 9 m/sec. 4 kmph = 4 x 18 5 m/sec = 10 9 m/sec. Let the
length of the train be x metres and its speed by y m/sec.
Then,
x
= 9 and
x y - 5 9 y - 10 9 = 10. 9y - 5 = x and 10(9y - 10) = 9x
9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Length of the train is 50 m.
or Let me explain in easy way. Here, on solving we get,
9y-x = 5.........eq no.1.
&90y-9x = 100......eq no.2.
Now, take eq no.1. 9y-x = 5. 9y = 5+x. y = 5+x/9.
Now put the value of y in eq no.2 then, 90y-9x = 100. 90(5+x/9)-9x = 100 ( here y= 5+x/9).
Now in L.H.S 90 is cancelled by 9 and become 10.

So, 10(5+x)-9x
= 100. 50+10x-
9x = 100. 50 +x
= 100. x = 100-
50. Answer x =
50.

Hope you'll get it

now.

28. A train overtakes two persons walking along a railway track. The first one
walks at 4.5
km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds
respectively to overtake them. What is the speed of the train if both the persons
are walking in the same direction as the train? [A]. 66 km/hr [B]. 72 km/hr [C].
78 km/hr [D]. 81 km/hr

Answer:
Option D

Explana
tion:

4.5 km/hr = 4.5 x 5 m/sec = 5 m/sec = 1.25

m/sec, and 18 4 5.4 km/hr = 5.4 x 5 m/sec = 3
m/sec = 1.5 m/sec. 18 2

Let the speed of the train be x

m/sec.

Then, (x - 1.25) x 8.4 = (x -

1.5) x 8.5

8.4x - 10.5 = 8.5x -

12.75

0.1x =
2.25
 x=
22.
5

Speed of the train = 22.5 x 18 km/hr = 81

km/hr. 5 or x is the length of the train; y is the velocity of the train x/y=t1
; x/y=t2 x/(y-1.25)=8.4 ; x/(y-1.5)=8.5

[4.5kmph=1.25m/s
;5.4kmph=1.5m/s]

x-8.4y=-
10.75..........(1) x-
8.5y=-
12.75..........(2)
solving the equ 1
&2

we get thge solution y=22.5m/s

there for ans; the speed of the train
y=22.5m/s=81kmph

29. A train travelling at 48 kmph completely crosses another train having half its
length and
travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway
platform in 45 seconds. The length of the platform is [A]. 400 m [B]. 450 m [C].
560 m [D]. 600 m

Answer:
Option A

Explana
tion:

Let the length of the first train be x

metres.

Then, the length of the second train is x metres. 2

Relative speed = (48 + 42) kmph = 90 x 5 m/sec = 25
m/sec. 18
[x + (x/2)] = 12 or 3x = 300 or x = 200. 25 2

Length of first train =

200 m.
 Let the length of platform be y
metres.

Speed of the first train = 48 x 5 m/sec = 40

m/sec. 18 3
(200 + y) x 3
= 45 40

600 + 3y =
1800

y=
400
m.

or According to the problem,

First let us take length of the first

train as "x"

So the length of the second train is half of the second train so it

is half of x So the total length is "(3/2)x"

and given that the two trains are travelling in opposite directions so that their
relative speed = (48+42)km/hr. now convert into m/s so it is 90*(5/18) =25 m/s.

from basic rule s

= d /t;

25 m/s = ((3/2)x)/ 12
sec by solving it we
get x = 200m

and given that time required to pass platform

is 45 sec

and length of platform =

z 48 * (5/18) = (200+z)
m/ 45 sec

by solving it we get finally

400 m
30. Two stations A and B are 110 km apart on a straight line. One train starts
from A at 7 a.m.
and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and
travels towards A at a speed of 25 kmph. At what time will they meet? [A]. 9 a.m.
[B]. 10 a.m. [C]. 10.30 a.m. [D]. 11 a.m.

Answer:
Option B

Explana
tion:

Suppose they meet x hours

after 7 a.m.

Distance covered by A in x hours =

20x km.
Distance covered by B in (x - 1) hours = 25(x
- 1) km.

20x + 25(x - 1)
= 110

45x =
135

x
=
3.

So, they meet at

10 a.m.

or Length of the track between starting position of train A starts at 7A.M and B Starts at 8A.M is
200 km.

Let's say A train travels with 20 kmph for 5

hours.

Distance covered by train A is =

100 km.
Train B Travels with 25 kmph for
4 hrs.

Distance covered by train B is

=100km.

A train => 7+5=12

noon.

B train => 8+4=12

noon.

If we consider 7 as X then 8 should become (X-1) when we

compare with the destination time.

or Let us consider first train it's speed is 20 km/hr.

So it covers 20 kms in
1 hour.

Starting from 7 am 1st train second train from 8 am

to 9 am.

At 8 am it covers 20 km at 9 am it covers 25 km. 9 am it covers 40 km 10 am it

covers 50 km.

10 am ===
60 km.

So at 10 am total distance covered by two trains is

60+50=110 km.

Which is the actual distance of separation between two train hence they meet each other
so simple.

31. Two, trains, one from Howrah to Patna and the other from Patna to
Howrah, start
 simultaneously. After they meet, the trains reach their destinations after 9 hours
and 16 hours respectively. The ratio of their speeds is: [A]. 2 : 3 [B]. 4 : 3 [C]. 6 :
7 [D]. 9 : 16

Answer:
Option B

Explana
tion:

Let us name the trains as A and

B. Then,

(A's speed) : (B's speed) = b : a = 16 :

9 = 4 : 3.

or Let train from Howrah to Patna (thp) speed is a kmph.

Let train from Patna to Howrah (tph) speed is

b kmph.

Total distance from h to p =

9a+16b.

Train starts simultaneously, hence when both train meets then both spend same time while
travel some distance.

Thp<------------16b----><-------9a--
--->tph.

Time through thp = Time

through tph.
16b/a = 9a/b.
Hence, a/b = 4/3.
Data suffiency 1:
Each of the questions given below consists of a statement and / or a question and
two statements numbered I and II given below it. You have to decide whether the
data provided in the statement(s) is / are sufficient to answer the given question.
Read the both statements and
• Give answer (A) if the data in Statement I alone are sufficient to answer the
question, while the data in Statement II alone are not sufficient to answer the
question.
• Give answer (B) if the data in Statement II alone are sufficient to answer the
question, while the data in Statement I alone are not sufficient to answer the
question.
• Give answer (C) if the data either in Statement I or in Statement II alone are
sufficient to answer the question.
• Give answer (D) if the data even in both Statements I and II together are not
sufficient to answer the question.
• Give answer(E) if the data in both Statements I and II together are necessary to
answer the question.
1. What is the speed of the train whose length is 210 metres?
I. The train crosses another train (Howrah Express/12869) of 300 metres length
running in
opposite direction in 10 seconds. II. The train crosses another train (Howrah
Express/12869) running in the same direction at
the speed of 60 km/hr in 30 seconds. [A]. I alone sufficient while II alone not
sufficient to answer [B]. II alone sufficient while I alone not sufficient to answer [C].
Either I or II alone sufficient to answer [D]. Both I and II are not sufficient to answer
[E]. Both I and II are necessary to answer
Answer: Option E
Explanation:
Time taken to cross the train, running in opposite directions = (l1 + l2) sec. (u + v)
10 = (210 + 300)
(u + v)
u + v = 51.
Time taken to cross the train, running in same direction = (l1 + l2) sec. (u - v)
30 = (210 + 300)
(u - 60 x (5/18)) u = 17 + 50
m/sec. 3
Thus, u and v can be obtained.
Correct answer is (E).
or Option E is okay, just see the instruction guys both statements together are necessary to answer this question as from stat-1
you will get the length of other train n using stat-2 data you can calculate the speed easily,
one thing that I find ambiguous is that both statements are contradicting as in 1st one train is
moving in opposite direction while in 2nd one same train is moving in same direction.
Each of the questions given below consists of a statement and / or a question and
two statements numbered I and II given belo decide whether the data provided in the
statement(s) is / are sufficient to answer the given question. Read the both
statements
• Give answer (A) if the data in Statement I alone are sufficient to answer the
question, while the data in Statement II al to answer the question.
• Give answer (B) if the data in Statement II alone are sufficient to answer the
question, while the data in Statement I al to answer the question.
• Give answer (C) if the data either in Statement I or in Statement II alone are
sufficient to answer the question.
• Give answer (D) if the data even in both Statements I and II together are not
sufficient to answer the question.
• Give answer(E) if the data in both Statements I and II together are necessary to
answer the question.
2. What is the length of a running train crossing another 180 metre long train running
in the opposite direction?
I. The relative speed of the two trains was 150 kmph. II. The trains took 9 seconds to
cross each other. [A]. I alone sufficient while II alone not sufficient to answer [B]. II
alone sufficient while I alone not sufficient to answer [C]. Either I or II alone sufficient
to answer [D]. Both I and II are not sufficient to answer [E]. Both I and II are
necessary to answer
Answer: Option E
Explanation:
Let the two trains of length a metres and b metres be moving in opposite directions
at u m/s and v m/s.
Time taken to cross each other = (a (u + + b) v) sec. Now, b = 180, u + v = 150 x 18 5
m/sec = 125 3 m/sec. 9 = a (125/3)
+ 180

a = (375 - 180) = 195 m.

Each of the questions given below consists of a statement and / or a question and
two statements numbered I and II given belo decide whether the data provided in the
statement(s) is / are sufficient to answer the given question. Read the both
statements
• Give answer (A) if the data in Statement I alone are sufficient to answer the
question, while the data in Statement II al to answer the question.
• Give answer (B) if the data in Statement II alone are sufficient to answer the
question, while the data in Statement I al to answer the question.
• Give answer (C) if the data either in Statement I or in Statement II alone are
sufficient to answer the question.
• Give answer (D) if the data even in both Statements I and II together are not
sufficient to answer the question.
• Give answer(E) if the data in both Statements I and II together are necessary to
answer the question.
3. What is the length of a running train?
I. The train crosses a man in 9 seconds. II. The train crosses a 240 metre long
platform in 24 seconds. [A]. I alone sufficient while II alone not sufficient to answer
[B]. II alone sufficient while I alone not sufficient to answer [C]. Either I or II alone
sufficient to answer [D]. Both I and II are not sufficient to answer [E]. Both I and II
are necessary to answer
Answer: Option E
Explanation:
Time taken by train to cross a man = Length Speed of of train train Speed = 9 l ....(i) Time taken
by train to cross a platform =
(Length of train + Length of platform) Speed = l + 240 ....(ii)
Speed of train 24 From (i) and (ii), we get l = l + 240 .
9
24

Thus, l can be obtained. So both I and II are necessary to get

the answer.

The correct answer

is (E).

or Train is passing a
man.

Obviously the length of train will be the same as the required distance to pass that man as
man has no length.
 9 sec to pass the man
(given).

24 sec to travel 240 m

(given).

So, speed = 240/24 =

10 m/s.

Hence, Length of train = Distance travelled in 9s =

9*10 = 90 m.

Data
suffiency
2:

Each of the questions given below consists of a question followed by three statements. You have to
question and the decide which of the statement(s) is/are necessary to answer the question.
1. What is the speed of
the train?
I. The train crosses a signal pole in 18 seconds. II. The
train crosses a platform of equal length in 36 seconds.
III. Length of the train is 330 metres. [A]. I and II only
[B]. II and III only [C]. I and III only [D]. III and either I or
II only [E]. Any two of the three

Answer:
Option D

Explana
tion:

Let the speed of the train be x

metres/sec.
Time taken to cross a signal pole = Length of the train Speed of the train Time taken to
cross a platform = (Length of the train + Length of the Platform)
Speed of the train
Length of train = 330 m.
I and III give, 18 = 330 x = 330 m/sec = 55 m/sec. x 18 3 II and III give, 36 = 2 x 330 x = 660
m/sec = 55 m/sec. x 36 3
Correct answer is (D).
Each of the questions given below consists of a question followed by three
statements. You have to study the question and the decide which of the statement(s)
is/are necessary to answer the question.
2. What is the speed of the train?
I. The train crosses a tree in 13 seconds. II. The train crosses a platform of length
250 metres in 27 seconds. III. The train crosses another train running in the same
direction in 32 seconds. [A]. I and II only [B]. II and III only [C]. I and III only [D]. Any
two of the three [E]. None of these
Answer: Option A
Explanation:
Let the speed of the train be x metres/sec.
Time taken to cross a tree = Length of the train Speed of the train Time taken to cross a
platform = (Length of the train + Length of the Platform)
Speed of the train I gives, 13 = 13x. x II gives 27 = l + 250
l

x 13x + 250 = 27 x x = 125 m/sec. 7

Thus I and II give the speed of

the train.

The correct answer is (A.) or 1. Let the

speed of the train be x metres/sec.

Velocity = length/time Therefore, time =

length/speed.

Length of train =
speed*time

=
13*x.................................
..(1).

2. Time=(length of train+length of platform)/speed

of train,

27 =
(length+250)/x.

= (13x+250)/x
(from 1).

= 17.85
m/sec.

Because of that I & II

correct
 DAta
Suffiency
3:

Each of these questions is followed by three statements. You have to study the question and all the
statements given to d information provided in the statement(s) is redundant and can be dispensed w
answering the given question.
1. At what time will the train reach city X from
city Y?
I. The train crosses another train of equal length of 200 metres and running in opposite directions in 1
seconds. II. The train leaves city Y and 7.15 a.m. for city X situated at a distance of 558 km. III. Th
200 metres long train crosses a signal pole in 10 seconds. [A]. I only [B]. II only [C]. III only [D]. II
III only [E]. All I, II and III are required.
Answer: Option D
Explanation:
From the statement I, we get length of the train is 200 metres (Redundant info while
comparing with Statement III). The r in this statement cannot be used for calculating
the speed of the train, because the two trains might run at different speed.
III gives, speed = 200 m/sec = 20 m/sec = 20 x 18
km/hr = 72 km/hr. 10 5 II gives, time taken = 558
hrs = 31 hrs = 7 3 hrs = 7 hrs 45 min. 72 4 4
So, the train will reach city X at 3 p.m.
Hence II and III only gives the answer.
or Firstly, as many others have pointed out, we have to tell which one or ones of the given pieces of information is or are
redundant and can be dispensed with while answering the question. According to this, option
A is the correct answer, because we can answer the question using only information II and
information III.
Secondly, if we were to tell which information are sufficient to answer the question, then the
correct answer will be D.I don't understand why some people are saying the correct answer
will be E in this case, do they have any doubt that the given solution is not able to find the
reaching time of the train? In other words, the solution is wrong? No friends, the "solution" is
correct.
Thirdly, @Prema:
Time taken to reach at station X is 7 hrs 45 mins.
Starting time = 7:15 am, so reaching time will be (7:15 am + 7 hrs 45 mins) which is nothing
but 3 pm.
Each of these questions is followed by three statements. You have to study the
question and all the three statements given to d information provided in the
statement(s) is redundant and can be dispensed with while answering the given
question.
2. What is the length of a running train P crossing another running train Q?
I. These two trains take 18 seconds to cross each other. II. These trains are running
in opposite directions. III. The length of the train Q is 180 metres. [A]. I only
[B]. II only [C]. III only [D]. All I, II and III are required [E]. Even with I, II and III, the
answer cannot be obtained.
Answer: Option E
Explanation:
Let the length of the train P be x metres.
II. These trains are running in opposite directions.
III. Length of the train Q is 180 m.
I. Time taken by P to cross Q = (180 + x) 18 = (180 + x)
Relative speed Relative speed
Thus, even with I, II and III, the answer cannot be obtained.
Correct answer is (E).

Time and Work

1. Work from Days:
If A can do a piece of work in n days, then A's 1 day's work = 1 . n
2. Days from Work:
If A's 1 day's work = 1 , then A can finish the work in n days. n
3. Ratio:
If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of times taken by A and B to finish a work = 1 : 3.
1. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days,
then the
fraction of the work that is left is : [A]. 1 4 [B]. 10 1 [C]. 15 7 [D]. 15 8 Answer: Option D
Explanation:
A's 1 day's work = 15 1 ; B's 1 day's work = 20 1 ; (A + B)'s 1 day's work = 15 1 + 20 1 = 60 7
. (A + B)'s 4 day's work = 60 7 x 4 = 15
7 . Therefore, Remaining work = 1 -

7 15 = 15 8 . Or For A:- 15 days for 1 job in 1 day 1/15 (part of the one job) for B:- 20 days for
1 job in 1 day 1/20 (part of the one job) FOR BOTH IN ONE DAY:- 1/15+1/20=7/60 FOR
BOTH IN 4 DAYS:- (7/60)*4=7/15(THEY HAVE DONE) THE REST PART OF THE JOB IS:-
1-(7/15)=8/15 (ANS)
2. A can lay railway track between two given stations in 16 days and B can do the
same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone
can do the job in: [A]. 9 1 5 days [B]. 9 2 5 days [C]. 9 3 days [D]. 10
5

Answer:
Option C

Explana
tion:

(A + B + C)'s 1 day's
work = 1 , 4 A's 1 day's
work = 1 , 16 B's 1 day's
work = 1 . 12
C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 5 . 4 16 12 4
48 = 9
48 48 So, C alone can do the work in
3 days.
55
Or "A" can do the 1/16 of the work in a day. "B"
can do the 1/12 of the work in a day. A + b + c =
1/4 of the work. 1/16 + 1/12 + c = 1/4. 3/48 + 4/
48 + c = 1/4. 7/48 + c = 1/4. C = 1/4 - 7/48 = 12-
7/48 = 5/48. C can do 5/48 of the work per day.
Therefore he can complete his work on 48/5 days
= 9 3/5.

3. A, B and C can do a piece of work in 20, 30 and 60 days

respectively. In how many days can A do the work if he is assisted by
B and C on every third day? [A]. 12 days [B]. 15 days [C]. 16 days
[D]. 18 days

Answer:
Option B

Explana
tion:

A's 2 day's work = 1 x 2 = 1 . 20 10 (A + B +

C)'s 1 day's work = 1 + 1 + 1 = 6 = 1 . 20 30 60
1 1 1
60 10 Work done in 3 days = + = . 10 10 5
Now, 1 work is done in 3 days.
5 Whole work will be done in (3 x 5) = 15 days.

Or A is working alone for two days, 3rd day he is

assisted by B and C.

A's 1 day work=1/20 A

working on 2
days=2*1/20=1/10

A+B+C working on 3rd day, so 1 day of working

together=1/20+1/30+1/60=6/60=1/10

So total work done till 3rd

day=1/10+1/10=2/10=1/5 So if in 3 days =
1/5 of work is completed.... Than, 3*5 days =
1/5*5 work will be completed. =15days

4. A is thrice as good as workman as B and therefore is able to finish

a job in 60
days less than B. Working together, they can
do it in: [A]. 20 days [B]. 22 1 days 2 [C]. 25
days [D]. 30 days

Answer:
Option B
 Explana
tion:

Ratio of times taken by A and B

= 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A

takes 1 day.

If difference of time is 2 days, B takes

3 days.

If difference of time is 60 days, B takes 3 x 60 =

90 days. 2

So, A takes 30 days to do

the work.

A's 1 day's work = 1 30 B's 1 day's work = 1

90 (A + B)'s 1 day's work = 1 + 1 = 4 = 2 30 90
90 45 A and B together can do the work in 45
= 22 1 days. 2 2

Or Given: A's time taken:B's time taken=1:3

So A's proportion of time

taken=1/(1+3)=>1/4*some x B's proportion of
time taken=3/(1+3)=>3/4*some x

As it is said that difference of time is

60 days

B's time-A's
time=60 =>
3x/4-x/4=60
=>x=120

So A's proportion of time taken

=x/4=120/4=30 days B's proportion of time
taken =3x/4=3*120/4=90 days

A's 1 day's work = 1/30 B's 1 day's work =

1/90 (A + B)'s 1 day's work = (1/30 +
1/90)= 4/90=2/45

A and B together can do the work in 45/2 = 22

1/2 days.

5. A alone can do a piece of work in 6 days and B alone in 8

days. A and B
 undertook to do it for Rs. 3200. With the help of C, they completed
the work in 3 days. How much is to be paid to C? [A]. Rs. 375 [B].
Rs. 400 [C]. Rs. 600 [D]. Rs. 800

Answer:
Option B

Explana
tion:

C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 1 . 3 6 8 3 24

1 1
24 A's wages : B's wages : C's wages = : :
1 = 4 : 3 : 1.
6 8 24
C's share (for 3 days) = Rs. 3 x 1 x 3200 =
Rs. 400. 24

Or A's wages : B's wages : C's wages = =A's

1 day's work:B's 1 day's work:C's 1 day's
work =1/6 : 1/8 : 1/24 =4 : 3 : 1.(multiple by
24..:1/6*24 : 1/8*24 : 1/24*24)

6. If 6 men and 8 boys can do a piece of work in 10 days while 26

men and 48
boys can do the same in 2 days, the time taken by 15 men and 20
boys in doing the same type of work will be: [A]. 4 days [B]. 5 days
[C]. 6 days [D]. 7 days

Answer:
Option A

Explana
tion:

Let 1 man's 1 day's work = x and 1 boy's 1 day's

work = y.

Then, 6x + 8y = 1 and 26x + 48y = 1 . 10 2 Solving

these two equations, we get : x = 1 and y = 1 . 100
15 + 20 = 1
200 (15 men + 20 boy)'s 1 day's work =
. 100 200 4

15 men and 20 boys can do the work

in 4 days.

Or 6x+8y=1/10
----- (i)
26x+48y=1/2 --
----(ii)
Multiply 1st equation into 6, then
we get: 36x+48y=1/10*6
26x+48y=1/2

Change the sign of 2nd

equation 36x+48y=3/5 -
26x-48y=-1/2

The
result is
10x=3/
5-1/2
10x=1/
10
x=1/10
0

Then apply x value into 1st

equation 6x+8y=1/10
6*1/10+8y=1/10 8y=4/100
y=1/200

7. A can do a piece of work in 4 hours; B and C together can do it in 3

hours, while
A and C together can do it in 2 hours. How long will B alone
take to do it? [A]. 8 hours [B]. 10 hours [C]. 12 hours [D]. 24
hours

Answer:
Option C

Explana
tion:

A's 1 hour's work = 1 ; 4 (B + C)'s 1

hour's work = 1 ; 3 (A + C)'s 1
hour's work = 1 . 2 (A + B + C)'s 1
hour's work = 1 + 1 = 7 . 4 3 12 B's 1
hour's work = 7 - 1 = 1 . 12 2 12

B alone will take 12 hours to do

the work.

Or A's 1 hour work is 1/4 (A+C)'s 1 hour work is 1/2

(B+C)'s 1 hour work is 1/3 so, A+C=1/2 ->X and
B+C=1/3 ->Y subtract X-Y we will get A-B=1/6 now,
substitute A's value in d equation u vl get B's value as
1/12. which is 1 day,s work of B... hence B alone
require 12 days...
 8. A can do a certain work in the same time in which B and C together
can do it. If A and B together could do it in 10 days and C alone in 50
days, then B alone could do it in: [A]. 15 days [B]. 20 days [C]. 25 days
[D]. 30 days

Answer:
Option C

Explana
tion:

(A + B)'s 1 day's work = 1 10 C's 1 day's

work = 1 50 (A + B + C)'s 1 day's work = 1 + 1
= 6 = 3 . .... (i) 10 50 50 25

A's 1 day's work = (B + C)'s 1 day's work .... (ii)

From (i) and (ii), we get: 2 x (A's 1 day's work) = 25 3 A's 1 day's work = 50 3 . B's 1 day's
work 10 1 - 50 3 = 50 2 = 25 1 . So, B alone could do the work in 25 days.

Or

In this problem

A's one day work is equal to (b+c)'s one day work A = (B+C)

So a+b+c become 2A here they taken instead of b+c= a

so A+B+C = A+ (B+C) = A+A becasue B+C=A 3/25 = 2* (A's one day work)

so 2* A's one day work

9.
s. He then calls in B and they together finish the remaining work in 3 days. How long B alone
? [A]. 23 days [B]. 37 days [C]. 37 [D]. 40 days

Answer:
Option C

Explana
tion:

Whole work is done by A in 20 x 5 = 25 days.

4 1
4 Now, 1 - i.e., work is done by A and B in
3 days. 5 5

Whole work will be done by A and B in (3 x 5) =

15 days.

A's 1 day's work = 1 , (A + B)'s 1 day's

work = 1 . 25 15
B's 1 day's work = 1 - 1 = 4 = 2 .
15 25 150 75
So, B alone would do the work in 75 = 37 1 days. 2 2

work =
days

for A: 80% work = 20 days 4/5 work =

20 days cross mul 1 work = 5/4 * 20
days 1 work = 25 days A's 25 days =
1 work ----------------------------->1

A+B remain work done in

3 days total work = 1 80%
work = 4/5 100% work = 1
100% - 80% = 1 - 4/5 =
1/5

for A+B:
work = days
1/5 work = 3
days cross
mul 1 work
= 15 days
dat is

A+B's 15 days = 1 work -------------------

-------->2
now we know A's and
A+B's work now find B's
work
apply A's in A+B's A+B 1
Days= 1/15 works A's 1 days
= 1/25 works---->from 1..

1/25 + B = 1/15 works B's

days = 1/15 - 1/25 Works
B's days= 2/75 works we
have to calc works cross
mul B's work = 75/2 days =
37 1/2 days

10. A machine P can print one lakh books in 8 hours, machine Q can
print the same
number of books in 10 hours while machine R can print them in 12
hours. All the machines are started at 9 A.M. while machine P is
closed at 11 A.M. and the remaining two machines complete work.
Approximately at what time will the work (to print one lakh books) be
finished ? [A]. 11:30 A.M. [B]. 12 noon [C]. 12:30 P.M. [D]. 1:00
P.M.

Answer:
Option D

Explana
tion:

(P + Q + R)'s 1 hour's work = 1 + 1 + 1 = 37 . 8 10 12 120 Work

done by P, Q and R in 2 hours = 37 x 2 = 37 . 120 60
Remaining work = 1 - 37 = 23 . 60 60 (Q + R)'s 1 hour's work =
1 + 1 = 11 . 11 work is done by Q and R in 1 hour.
10 12 60 Now,
23 work will be done by Q and R in 60 x 23 = 23 hours 2
60 So,
hours. 60 11 60 11

So, the work will be finished approximately 2 hours after 11 A.M.,

i.e., around 1 P.M.

Or P 1hrs
work 1/8 Q
1hrs work
1/10 R 1hrs
work 1/12

p worked for 2 hrs so 2*1/8

suppose Q and r worked for
'x' hrs
then,
2*1/8+(1/10)*x+(1/12)
x = 1 x=4.09 ans
9+4.09 = 1pm

11. A can finish a work in 18 days and B can do the same work in 15 days. B
worked for 10
days and left the job. In how many days, A alone can finish the
remaining work? [A]. 5 [B]. 5 1 2 [C]. 6 [D]. 8

Answer:
Option C

Explana
tion:

B's 10 day's work = 1 x 10 = 2

. 15 3 Remaining work = 1 - 2
= 1 . 3 3 Now, 1 work is done
by A in 1 day. 18
1 work is done by A in 18 x 1 = 6 days. 3 3

Or See, B complete his work in 15 days so split in 3 so

we get 1:1:1.

Then he done the work of 10 days, so only last one

remaining.1/3.

Now, A finish the whole work in 1/18. He need to done

work in 1/3.

So 18*1/3 = 6
days.

12. 4 men and 6 women can complete a work in 8 days, while 3 men and 7
women can
complete it in 10 days. In how many days will 10 women
complete it? [A]. 35 [B]. 40 [C]. 45 [D]. 50

Answer:
Option B

Explana
tion:

Let 1 man's 1 day's work = x and 1 woman's 1 day's

work = y.
 Then, 4x + 6y = 1 and 3x +
7y = 1 .
8 10 Solving the two equations, we get: x = 11 , y = 1
400 400 1 woman's 1 day's work = 1 . 400 10 women's 1 day's work = 1 x 10 = 1 . 400 40
Hence, 10 women will complete the work in 40 days.
Oe If 4 men and 6 women can complete a work in 8 days 4 men and 1 women can complete
a work in=6* 8 days 1 men and 1 women can complete a work in=4*6* 8 days 1 men and 7
women can complete a work in=4*6*8/7 days 3 men and 7 women can complete a work
in=4*6*8/(3*7) days =64/7days which is not 10 days as given in the question
13. A and B can together finish a work 30 days. They worked together for 20 days
and then B left. After another 20 days, A finished the remaining work. In how many
days A alone can finish the work? [A]. 40 [B]. 50 [C]. 54 [D]. 60
Answer: Option D
Explanation:
(A + B)'s 20 day's work = 1 x 20 = 2 . 30 3 Remaining work = 1 - 2 = 1 . 3 3 Now, 1 work is
done by A in 20 days. 3
Therefore, the whole work will be done by A in (20 x 3) = 60 days.
14. P can complete a work in 12 days working 8 hours a day. Q can complete the
same work in
8 days working 10 hours a day. If both P and Q work together, working 8 hours a
day, in how many days can they complete the work? [A]. 5 5 11 [B]. 5 6 11
[C]. 6 5 11 [D]. 6 6 11

Answer:
Option A

Explana
tion:

P can complete the work in (12 x 8) hrs.

= 96 hrs.

Q can complete the work in (8 x 10) hrs. =

80 hrs.

P's1 hour's work = 1 and Q's 1 hour's work = 1 .

1 1 11 .
96 80 (P + Q)'s 1 hour's work = + = 96 80
480
480 So, both P and Q will finish the work in
hrs. 11
Number of days of 8 hours each = 480 x 1 = 60 days = 5
5 days.
11 8 11 11

Or P can do the work in 12days. He do per

day 8 hours.

P can do work in total

hours is:96.
Same as Q can do work
in:80hours.

P's one day work

is:1/96.

Q's one day work

is:1/80.

P+q one day work

is:1/96+1/80=11/480.

P+q work
is:480/11.

P+q can done 8 hours per

day:480/11*1/8.

15. 10 women can complete a work in 7 days and 10 children take 14 days to
complete the
work. How many days will 5 women and 10 children take to complete
the work? [A]. 3 [B]. 5 [C]. 7 [D]. Cannot be determined [E]. None of
these

Answer:
Option C
Explana
tion:

1 woman's 1 day's work = 1 70 1 child's 1 day's work =

1 140 (5 women + 10 children)'s day's work = 5 + 10 = 1

+ 1 = 1 70 140 14 14 7

5 women and 10 children will complete the work in

7 days.

O
r

10 women's one day work

=1/7 So 5 women's one day
work=1/14 and 10 child's
one day work =1/14

So 5 women's and 10 childrens one

day work is
= 1/14 +
1/14 =
2/14 =
1/7

Ans: 7
days.

16. X and Y can do a piece of work in 20 days and 12 days respectively. X

started the work
alone and then after 4 days Y joined him till the completion of the work. How
long did the work last? [A]. 6 days [B]. 10 days [C]. 15 days [D]. 20 days

Answer:
Option B

Explana
tion:

Work done by X in 4 days = 1 x 4 = 1 . 20 5

Remaining work = 1 - 1 = 4 . 5 5 (X + Y)'s 1
day's work = 1 + 1 = 8 = 2 . 20 12 60 15 Now, 2 work
is done by X and Y in 1 day. 15 So, 4 work will
be done by X and Y in 15 x 4 = 6 days. 5 2 5

Hence, total time taken = (6 + 4) days =

10 days.

Or In 1 day 1/20
th work.

Let us assume a takes x days to

complte it

As B joins 4 days later he has only x-4 days

remaining.

They both work respectively with their capacities and finish the one
complete work

H
e
n
c
e

(1/20th work) * x days + (1/12th work) * (x-4) days = 1

full work
=> x/20 + (x-
4)/12 = 1

=> x =
10days

17. A is 30% more efficient than B. How much time will they, working
together, take to
complete a job which A alone could have done in 23
days? [A]. 11 days [B]. 13 days [C]. 20 3 days 17 [D].
None of these

Answer:
Option B

Explana
tion:

Ratio of times taken by A and B = 100 : 130 =

10 : 13.

Suppose B takes x days to do

the work.

Then, 10 : 13 :: 23 : x x = 23 x 13 x = 299 . 10 10 A's 1

day's work = 1 ; 23 B's 1 day's work = 10 . 299 (A +
B)'s 1 day's work = 1 + 10 = 23 = 1 . 23 299 299 13

Therefore, A and B together can complete the work in

13 days.

18. Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type
32 pages on a
computer, while Kumar takes 5 hours to type 40 pages. How much time will
they take, working together on two different computers to type an
assignment of 110 pages? [A]. 7 hours 30 minutes [B]. 8 hours [C]. 8
hours 15 minutes [D]. 8 hours 25 minutes

Answer:
Option C

Explana
tion:

Number of pages typed by Ravi in 1 hour = 32 =

16 .
6 3 Number of pages typed by Kumar in 1
hour = 40 = 8. 5 Number of pages typed by both
in 1 hour = 16 + 8 = 40 . 3 3
Time taken by both to type 110 pages = 110 x 3 hours
1
40 = 8 hours (or) 8 hours 15 minutes. 4

Or No of pages typed/Hours=40/3/1=40/3-----First case No of

pages typed/Hours=110/x-----------second
case

The ratio would be same in both

the cases

40/3=1
10/x
Theref
ore

x=110*3/40=8*1/
4 hrs

19. A, B and C can complete a piece of work in 24, 6 and 12 days

respectively. Working
together, they will complete the same work in:
[A]. 1 day 24 [B]. 7 day 24 [C]. 3 3 days 7 [D]. 4
days

Answer:
Option C

Explana
tion:

Formula: If A can do a piece of work in n days, then A's 1 day's

work = 1 . n (A + B + C)'s 1 day's work = 1 + 1 + 1 = 7 .
24 6 12 24 Formula: If A's 1 day's work = 1 , then A can finish the work in n days. n
So, all the three together will complete the job in 24
days = 3 3 days. 7 7
Or A's work be x, B's work be y C's work be z
Total work done by A,B,C(A+B+C)=(X*Y*Z)/(XY+YZ+XZ)
Solution is: x=12 y=6 z=24
A+B+C=(12*6*24)/(12*6+6*24+24*12)
= 24/7
= 3 and (3/7)
20. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than
Sakshi. The
number of days taken by Tanya to do the same piece of work is: [A]. 15 [B]. 16 [C].
18 [D]. 25
Answer: Option B
Explanation:
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.
Suppose Tanya takes x days to do the work.
5 : 4 :: 20 : x x = 4 x 20
5
x = 16 days.
Hence, Tanya takes 16 days to complete the work.
Or The given answer is correct.
Sakshi's one day work=1/20 Tanya's one day work
=(1/20 + 25% of 1/20) = 1/20+1/80 = 1/16.

So Tanya can complete the work in

16 days.

21. A takes twice as much time as B or thrice as much time as C to finish a

piece of work. Working together, they can finish the work in 2 days. B can do
the work alone in: [A]. 4 days [B]. 6 days [C]. 8 days [D]. 12 days

Answer:
Option B

Explana
tion:

Suppose A, B and C take x, x and x days respectively to

finish the work. 2 3 Then, 1 + 2 + 3 = 1 x x x 2 6 = 1 x 2

x=
12
.

So, B takes (12/2) = 6 days to finish

the work.

Or B=2A C=3A
A+B+C=2days
A+2A+3A=2days
so,6A=2days A only takes
(6*2)=12 days B=2A,so B
only takes (12/2)=6days

22. A and B can complete a work in 15 days and 10 days respectively. They
started doing the work together but after 2 days B had to leave and A alone
completed the remaining work. The whole work was completed in : [A]. 8 days
[B]. 10 days [C]. 12 days [D]. 15 days

Answer:
Option C

Explana
tion:
 (A + B)'s 1 day's work = 1 + 1
=1.
15 10 6 Work done
by A and B in 2 days = 1 x 2 = 1 . 6 3
Remaining work = 1 - 1 = 2 . 3 3 Now, 1
work is done by A in 1 day. 15
2 work will be done by a in 15 x 2 = 10 days. 3 3

Hence, the total time taken = (10 + 2) =

12 days.

Or A's 1 day work=1/15 B's 1 day work=1/10 now,B left after 2 days then 1/10*2=1/5
remaining work is (1-1/5)=4/5 4/5 work is left by B then A has to do remaining work
(1/15*5/4)=1/12 this is A's 1 day work after B left work now A completes work in 12 days...

23. A and B can do a piece of work in 30 days, while B and C can do the same
work in 24 days
and C and A in 20 days. They all work together for 10 days when B and C
leave. How many days more will A take to finish the work? [A]. 18 days
[B]. 24 days [C]. 30 days [D]. 36 days

Answer:
Option A

Explana
tion:

2(A + B + C)'s 1 day's work = 1 + 1 + 1 = 15 =

1.
30 24 20 120 8 Therefore, (A + B + C)'s 1
day's work = 1 = 1 . 2 x 8 16 Work done by A,
B, C in 10 days = 10 = 5 . 16 8 Remaining
work = 1 - 5 = 3 . 8 8 A's 1 day's work = 1 - 1 =
1. 1
16 24 48 Now, work is done by A in 1 day.
3 3
48 So, work will be done by A in 48 x = 18
days. 8 8
O
r

A+B+C one day work

= 1/16. Given B+C =
1/24.

Therefore A+B+C
= 1/16. A+1/24 =
1/16. A = 1/16-
1/24.
 A=
1/48
.

24. A works twice as fast as B. If B can complete a work in 12 days independently,

the number
of days in which A and B can together finish the
work in : [A]. 4 days [B]. 6 days [C]. 8 days [D].
18 days

Answer:
Option A

Explana
tion:

Ratio of rates of working of A and B

= 2 : 1.

So, ratio of times taken

= 1 : 2.

B's 1 day's work

= 1 . 12
A's 1 day's work = 1 ; (2 times of B's work)
1 1 3 1
6 (A + B)'s 1 day's work = + = = . 6
12 12 4

So, A and B together can finish the work in

4 days.

Or Suppose B completes 1
work in x days.

So B completed work in 1 day =

1/x.............1.

Now A completes 1 work = x/2 (Cz A is twice

faster than B).

So A completed work in 1 day =

2/x.............2.

Together their Work = 1/x

+ 2 /x. Given x = 12.

S
o
 ,

Together their Work = 1/12 +

2 /12.

== 1/12 +
1/6. ==1/4
or 4 days.

24. A works twice as fast as B. If B can complete a work in 12 days independently,

the number
of days in which A and B can together finish the
work in : [A]. 4 days [B]. 6 days [C]. 8 days [D].
18 days

Answer:
Option A

Explana
tion:

Ratio of rates of working of A and B

= 2 : 1.

So, ratio of times taken

= 1 : 2.

B's 1 day's work

= 1 . 12
A's 1 day's work = 1 ; (2 times of B's work)
1 1 3 1
6 (A + B)'s 1 day's work = + = = . 6
12 12 4

So, A and B together can finish the work in

4 days.

Or let x=2(bcz A is twice as fast as B) n=12(bcz B

completes the work in 12 days) use the formula:A&B
together do the work in p days as follows p=n/x+1
=12/3 =4days

25. Twenty women can do a work in sixteen days. Sixteen men can complete the
same work in
fifteen days. What is the ratio between the capacity of a man and
a woman? [A]. 3 : 4 [B]. 4 : 3 [C]. 5 : 3 [D]. Data inadequate

Answer:
Option B
 Explana
tion:

(20 x 16) women can complete the work

in 1 day.
1 woman's 1 day's work = 1 . 320
(16 x 15) men can complete the work in 1 day.
1 man's 1 day's work = 1 240 So, required ratio = 1 : 1
240 320 = 1 : 1 3 4 = 4 : 3 (cross multiplied)
Or 25. Twenty women can do a work in sixteen days. Sixteen men can complete the
same work in
fifteen days. What is the ratio between the capacity of a man and a woman? [A]. 3 :
4 [B]. 4 : 3 [C]. 5 : 3 [D]. Data inadequate
Answer: Option B
Explanation:
(20 x 16) women can complete the work in 1 day.
1 woman's 1 day's work = 1 . 320
(16 x 15) men can complete the work in 1 day.
1 man's 1 day's work = 1 240 So, required ratio = 1 : 1
240 320 = 1 : 1 3 4 = 4 : 3 (cross multiplied)
26. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B
and C
together can finish it in 6 days. A and C together will do it in : [A]. 4 days [B]. 6 days
[C]. 8 days [D]. 12 days

Answer:
Option C

Explana
tion:

(A + B + C)'s 1 day's
work = 1 ; 6 (A + B)'s 1
day's work = 1 ; 8 (B +
C)'s 1 day's work = 1 . 12
(A + C)'s 1 day's work = 2 x 1 - 1
+ 1 6 8 12 = 1 - 5 3 24 = 3 24 = 1 .
8

So, A and C together will do the work in

8 days.

Or (A + B + C)'s 1 day's
work = 1/6

(A + B)'s 1 day's
work = 1/8
(B + C)'s 1 day's work
= 1/12

so c's 1 day's work=1/6-1/8=1/24

and a's 1 day's work=1/6-
1/12=1/12 and b's 1 day
work=1/6(1/24+1/12)=1/4

so a and c 1'day
work=1/12+1/24=1/8

27. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the
work but are
forced to leave after 3 days. The remaining work was
done by A in: [A]. 5 days [B]. 6 days [C]. 10 days [D]. 10
1 days
2

Answer:
Option C

Explana
tion:
(B + C)'s 1 day's work = 1 + 1 = 7 . 9 12 36
Work done by B and C in 3 days = 7 x 3
= 7 . 36 12 Remaining work = 1 - 7 = 5 . 12 12
Now, 1 work is done by A in 1 day. 24 So,
5 work is done by A in 24 x 5 = 10 days.

O
r

A
=
24
.B
=
9.
C
=
12
.

B & C started after 3 days they leave (The do

only 3 days).

Total
work = X.

A joined after 3 days X-3 (He finished

the work).
 = X-3/24 + 3/9 +
3/12 = 1.

To solve this we get

X = 13.

A=
X-
3.

=
13
-
3.

= 10
days.

28. X can do a piece of work in 40 days. He works at it for 8 days and then Y
finished it in 16
days. How long will they together take to complete
the work? [A]. 13 1 days 3 [B]. 15 days [C]. 20 days
[D]. 26 days

Answer:
Option A

Explana
tion:

Work done by X in 8 days = 1 x 8

= 1 . 40 5 Remaining work = 1 - 1 =
4.
5 5 Now, 4 work is done by Y in
16 days.
5 Whole work will be done by Y in 16 x 5 =
20 days. 4
X's 1 day's work = 1 , Y's 1 day's work = 1 . 40 20 (X + Y)'s 1
day's work = 1 + 1 = 3 . 40 20 40 Hence, X and Y will together
complete the work in 40 = 13 1 days. 3 3

O
r

x's speed of work is 40, so work in 1 day

is 1/40.

x does 8 days and leaves, so work done is

8*(1/40) = 1/5.
x does only 1/5 of the work , so remaining work to be done is 4/5 (1-
1/5 = 4/5).

y's speed of work is not given, let us take it as 'K'. but he completes the remaining 4/5
work in 16 days.

So 16*(1/K)=4/5 which gives

K = 20.

Now both together takes ( x speed of work + y speed

of work).

1/40 + 1/20 = 3/40 = 1/(40/3) =

1/(13 1/3).

So the ans is
13 1/3.

29. A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can
be done by A alone in : [A]. 9 1 days 3 [B]. 11
days [C]. 12 1 days 4 [D]. 16 1 days 3

Answer:
Option B

Explana
tion:

(A's 1 day's work) : (B's 1 day's work) = 7 : 1 =

7 : 4. 4

Let A's and B's 1 day's work be 7x and 4x

respectively.

Then, 7x + 4x = 1 11x = 1 x = 1 .
7 7 77 A's 1 day's work = 1 x 7
1
= . 77 11

Or A and B collectively can do the

work in 7 days so their one day work
is 1/7 A+B=1/7-------(1) A is 7/4 times
efficient then B which means

A=(7/4)B ----------
or B=(4/7)A ------------(2)
put the value of
(2)in (1)
(4/7)*B+B=1/7
B=1/11 THIS IS HIS ONE
DAY WORK ALONE B CAN
FINISH IN 11 DAY

29. A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can
be done by A alone in : [A]. 9 1 days 3 [B]. 11
days [C]. 12 1 days 4 [D]. 16 1 days 3

Answer:
Option B

Explana
tion:

(A's 1 day's work) : (B's 1 day's work) = 7 : 1 =

7 : 4. 4

Let A's and B's 1 day's work be 7x and 4x

respectively.

Then, 7x + 4x = 1 11x = 1 x = 1 . 7 7 77
A's 1 day's work = 1 x 7 = 1
. 77 11 Or A+B=1/7 7A+7B=1-----1

A=7/4
B
4A=7B
-----2

sub 2 in 1
7A+4A=1 (Since
7B=4A) therefore
11A=1 A=1/11

therefore A can finish in

11 days

30. A and B together can do a piece of work in 30 days. A having worked for
16 days, B
finishes the remaining work alone in 44 days. In how many days shall B
finish the whole work alone? [A]. 30 days [B]. 40 days [C]. 60 days [D]. 70
days

Answer:
Option C

Explana
tion:
 Let A's 1 day's work = x and B's 1 day's
work = y.

Then, x + y = 1 and 16x + 44y = 1. 30 Solving

these two equations, we get: x = 1 and y = 1
60 60 B's 1 day's work = 1 . 60

Hence, B alone shall finish the whole work in

60 days.

O
r

A's 1 day work ,consider X B's 1 day work

,consider Y (A+B) 1 day work=(X+Y)=1/30 next
condition: A works for 16 days=16*X B works for
44 days for remaining work to complete=44*Y to
complete whole work;16X+44Y=1 by solving both
equations ,we get X=1/60,Y=1/60 B can complete
work in 60 days.

Data
suffiency
1:

Each of the questions given below consists of a statement and / or a question and two
statements numbered I
decide whether the data provided in the statement(s) is / are sufficient to answer the given questio
the both statement

• Give answer (A) if the data in Statement I alone are sufficient to answer the question, while th
Statement II to answer the question.
• Give answer (B) if the data in Statement II alone are sufficient to answer the question, while t
Statement I a to answer the question.
• Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answ
the question.
• Give answer (D) if the data even in both Statements I and II together are not sufficient to answ
the question.
• Give answer(E) if the data in both Statements I and II together are necessary to answer
the question.

1. A and B together can complete a task in 7 days. B alone can do it in 20 days. What part of the
carried out by A
I. A completed the job alone after A and B worked together for 5 days. II. Part of
the work done by A could have been done by B and C together in 6 days. [A].
I alone sufficient while II alone not sufficient to answer [B]. II alone sufficient
while I alone not sufficient to answer [C]. Either I or II alone sufficient to
answer [D]. Both I and II are not sufficient to answer [E]. Both I and II are
necessary to answer

Answer:
Option A

Explanat
ion:

B's 1 day's work = 1 20

(A+ B)'s 1 day's work =
1 7 I. (A + B)'s 5 day's

work = 5 7 Remaining
work = 1 - 5 = 2 . 7 7 2
work was carried by A. 7

II. is
irrelevant.

Correct answer is (A). Or In this ques no doubt option A is correct, but I guess the
explanation given is correct only if it's asked to find out part of work done by A alone.

But ques is wht part of work ws carried out by A(alone + A's contribution when both A
& B worked together)which can be calculated as

B's 1 day's work =

1/20 (A+ B)'s 1
day's work = 1/7
=> A's 1 day's work = 1/7 - 1/20 =
13/140 => A's 5 day's work =
13/28

Now , (A + B)'s 5 day's

work = 5/7

Remaining work = 1 -
5/7 = 2/7

=> 2/7 work was carried by

A alone

a
n
d

Total part of work carried by A =

2/7+13/28= 3/4.
 Each of the questions given below consists of a statement and / or a question and two
statements numbered I decide whether the data provided in the statement(s) is / are sufficient
to answer the given question. Read the

• Give answer (A) if the data in Statement I alone are sufficient to answer the question,
while the data i to answer the question.
• Give answer (B) if the data in Statement II alone are sufficient to answer the question,
while the data to answer the question.
• Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to
answer the q
• Give answer (D) if the data even in both Statements I and II together are not sufficient to
answer the q
• Give answer(E) if the data in both Statements I and II together are necessary to answer
the question.

2. How long will Machine Y, working alone, take to produce x

candles?
I. Machine X produces x candles in 5 minutes. II. Machine X and Machine Y working
at the same time produce x candles in 2 minutes. [A]. I alone sufficient while II
alone not sufficient to answer [B]. II alone sufficient while I alone not sufficient to
answer [C]. Either I or II alone sufficient to answer [D]. Both I and II are not
sufficient to answer [E]. Both I and II are necessary to answer

Answer:
Option E

Explanat
ion:

I. gives, Machine X produces x candles in 1 min. 5 II.

gives, Machine X and Y produce x candles in 1 min.
3x candles in 1 min.
2 From I and II, Y produces x - x =
2 5 10 3x candles are produced by Y in 1 min. 10 x candles will be produced
by Y in 10 x x min = 10 min. 3x 3

Thus, I and II both are necessary to get

the answer.

Correct answer
is (E).

Or Ram and Hari can do a piece of work in 18 days . If Hari works alone for the last
15 days then it is completed in 27 days . In how many days Ram can do the whole
work

Data
suffeincu
2:
 Each of the questions given below consists of a question followed by three statements. You
have to study the decide which of the statement(s) is/are necessary to answer the question.
1. In how many days can 10 women finish
a work?
I. 10 men can complete the work in 6 days. II. 10 men and 10 women together can complete the work in 3 3 days 7 III. If
10 men work for 3 days and thereafter 10 women replace them, the remaining work in
completed i [A]. Any two of the three [B]. I and II only [C]. II and III only [D]. I and III only [E].
None of these

Answer:
Option A

Explana
tion:

I. (10 x 6) men can complete the work

in 1 day.

1 man's 1 day's
work = 1 60

II. 10 x 24 men + 10 x 24 women can complete the work in 1

day. 7 7
240 men's 1 day work + 240 women's 1 day work = 1. 7 7 240 x 1
+ 240 women's 1 day's work = 1. 7 60 7 240 women's 1 day's work = 1
3 7
- 4 = 3 7 7 7 10 women's 1 day's work = x x 10 =
1 7 240 8

So, 10 women can finish the work in

8 days.

III. (10 men's work for 3 days) + (10 women's work for 4
days) = 1

(10 x 3) men's 1 day's work + (10 x 4) women's 1 day's

work = 1

30 men's 1 day's work + 40 women's 1 day's

work = 1

Thus, I and III will give us the

answer.

And, II and III will give us the

answer.
 Correct answer
is (A).

O
r

1 men's 1 day work = 1/10*6

= 1/60.

(10 men + 10 women)'s 1 day work

= 7/24.

1/10*6*10 + 10 women
= 7/4.

So 10 women's 1 day work = 7/4-1/6 =

3/24 = 1/8.

Data suffiency 3: Each of these questions is followed by three statements. You have to study the
question and all the three state information provided in the statement(s) is redundant and can
be dispensed with while answering the given q 1. 8 men and 14 women are working together in
a field. After working for 3 days, 5 men and 8 women leav
be required to complete the
work?
I. 19 men and 12 women together can complete the work in 18 days. II. 16 men can
complete two-third of the work in 16 days. III. In 1 day, the work done by three
men in equal to the work done by four women. [A]. I only [B]. II only [C]. III only
[D]. I or II or III [E]. II or III only

Answer:
Option D

Explanat
ion:

Clearly, I only gives the

answer.
Similarly, II only gives the answer.
And, III only gives the answer.
Correct answer is (D).
Simple Interest - Important Formulas
1. Principal:
The money borrowed or lent out for a certain period is called the principal or
the sum.
2. Interest:
Extra money paid for using other's money is called interest.
3. Simple Interest (S.I.):
If the interest on a sum borrowed for certain period is reckoned uniformly,
then it is called simple interest.
Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then
(i). Simple Intereest =
PxRxT
100
(ii). P =
100 x S.I.
;R=
100 x S.I.
and T =
100 x S.I.
.RxTPxTPxR
Read more:
3. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5
years. What
is the sum? [A]. Rs. 4462.50 [B]. Rs. 8032.50 [C]. Rs. 8900 [D]. Rs. 8925
[E]. None of these
Answer: Option D
Explanation:
Principal = Rs. 100 x 4016.25
9 x 5 = Rs. 401625
45 = Rs. 8925. Simple interest = P*T*R/100,
P = 100*S.I/T*R,
= 100*4016.25/5*9 = 8925.
Principal means sum here.
4. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at
4.5% per
annum of simple interest? [A]. 3.5 years [B]. 4 years [C]. 4.5 years [D]. 5 years
Answer: Option B
Explanation:
Time = 100 x 81
years = 4 years. 450 x 4.5
S.I = 81, P = 450, R = 4.5.
T = S.I*100/P*R.
T = 81*100/450*4.5 (Cancel 100/450 with 5 and 81 with 9).
T = 9*2/4.5. T = 18/4.5 => 180/45.
T = 4 Years.
5. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate
of interest. If
she paid Rs. 432 as interest at the end of the loan period, what was the rate of
interest? [A]. 3.6 [B]. 6 [C]. 18 [D]. Cannot be determined [E]. None of these
Answer: Option B
Explanation:
Let rate = R% and time = R years.
Then, 1200 x R x R = 432 100
12R2 = 432
R2 = 36
R = 6.
6. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple
interest. What is
the rate of interest? [A]. 3% [B]. 4% [C]. 5% [D]. 6% [E]. None of these
Answer: Option D
Explanation:
S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate = 100 x 3000
% = 6% 12500 x 4
S.I per annum = (15500-12500)/4 = 750.
Rate = (S.I*100)/(P*T).

=
(750*100)/(12500
*4).

= 75000/50000
= 1.5.

Since interest is for four years, multiply by 4, thus;

1.5*4 yrs = 6.

Therefore are (rate)

= 6%.

7. An automobile financier claims to be lending money at simple interest, but he

includes the interest every six months for calculating the principal. If he is
charging an interest of 10%, the effective rate of interest becomes: [A]. 10% [B].
10.25% [C]. 10.5% [D]. None of these

Answer:
Option B

Explana
tion:

Let the sum be Rs. 100.

Then,

S.I. for first 6 months = Rs. 100 x 10 x 1 = Rs. 5

105 x 10 x 1 =
100 x 2 S.I. for last 6 months = Rs.
Rs. 5.25 100 x 2

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) =

Rs. 110.25

Effective rate = (110.25 - 100) =

10.25%
Let the sum be Rs. 100. Then, for six month time will be (6/12) year which
become 1/2 year.

S.I. for first 6 months = Rs. (100 x 10 x

1)/100*2 = Rs. 5.

Now Principal for next 6 months will

100+5 = 105.

S.I. for next 6 months = Rs. (105 x 10 x 1)100*2

= Rs. 5.25.

Total interest in a year

10.25.

Apply
formula:

S.I. =
P*r*t/100.

Put value for a

year now.

10.25 =
100*r*1/100.

R=
10.25*100/100*
1.

R=
10.25
%.

8. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple
interest at the same
rate of interest and received Rs. 2200 in all from both of them as interest. The
rate of interest per annum is: [A]. 5% [B]. 7% [C]. 7 1 % 8 [D]. 10%

Answer:
Option D

Explana
tion:

Let the rate be

R% p.a.
 Then, 5000 x R x 2 + 3000 x R x 4 = 2200. 100
100

100R + 120R =
2200

R = 2200 =
10. 220

Rate =
10%.

Lets assume that rate

% = x.

(If you have taken 5000 on 1% then S.I per year = 50 Rs (1 Rs for 100 then 50
hundreds so 50x100(5000)=50 Rs, if 50 per single year so for 2 years it would
be 100)(Similarly for 3000).

Then S.I on 5000 for 2 years =

100x. Then S.I on 3n000 for 4
years = 120x. From the
problem 100x+120x = 2200.

Then 220x =
2200.

x=10. I hope
this is clear.

9. A sum of Rs. 725 is lent in the beginning of a year at a certain rate of

interest. After 8
months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At
the end of the year, Rs. 33.50 is earned as interest from both the loans. What
was the original rate of interest? [A]. 3.6% [B]. 4.5% [C]. 5% [D]. 6% [E]. None
of these

Answer:
Option E

Explana
tion:

Let the original rate be R%. Then, new rate

= (2R)%.
 N
o
t
e
:

Here, original rate is for 1 year(s); the new rate is for only 4 months
i.e. year(s).

725 x R x 1 + 362.50 x 2R x 1 =
33.50 100 100 x 3

(2175 + 725) R = 33.50 x

100 x 3

(2175 + 725) R =
10050

(2900)R =
10050

R = 10050 =
3.46 2900

Original rate =
3.46%

(725 x R x 1 /100) + (362.50 x 2R x 1 /100 x 3 )

= 33.50
(725 x 1 /100 + 362.50 x 2 /100 x 3) R
= 33.50

(725 x 3 + 725 / 100 x 3) R =

33.50

(2175 + 725 ) R = 33.50 x

100 x 3

(2900) R =
10050

R=
10050/290
0
 R=
3.46%

Let the original rate is r%, then new rate is 2r. here original rate is for only
8 months i.e 2/3; new rate is for 4 month i.e 1/3year(s).
=>{(725*r*2)/(100*3)}+{(362.50*2r*1)/(100*3)}=33.50
=>4.8333333333r+2.4166666667r=33.50 =>7.25r=33.50 =>r=33.50/7.25
=>r=4.6206896552 i.e original rate=4.62%

10. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3
years he had to
pay Rs. 5400 interest only for the period. The principal amount borrowed
by him was: [A]. Rs. 2000 [B]. Rs. 10,000 [C]. Rs. 15,000 [D]. Rs. 20,000

Answer:
Option C

Explana
tion:

Principal = Rs. 100 x 5400 = Rs.

15000. 12 x 3

36% ----> 5400 then 1% ---->

5400/36 =150. 100%---->x So, x =
150 * 100. =15000.

11. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8
years at the same
rate of simple interest. The rate of interest per
annum is: [A]. 5%
[B]. 8% [C]. 12% [D]. 15%
Answer: Option C
Explanation:
S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.
S.I. for 5 years = Rs. 2205 x 5 = Rs. 3675 3
Principal = Rs. (9800 - 3675) = Rs. 6125.
Hence, rate = 100 x 3675
% = 12% 6125 x 5 SI For 3 years = 12500-9800 = 2205. SI For 1 year = 2205/3 = 735.
So, SI For 5 years = 5*735 = 3675.
Principal for 5 years = 9800-3675 = 6125. Now calculate rate for 5 years =
(3675*100)/(6125*5) = 12%.
Or THE DIFFERENCE BETWEEN GIVEN YEARS 5 AND 8 IS 3, SO,
S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205. S.I. for 1 year = Rs. (2205/3) = Rs 735. S.I.
for 5 years = 735*5 = Rs. 3675. Principal = Rs. (9800 - 3675) = Rs. 6125.
Hence, rate = 12%.
12. What will be the ratio of simple interest earned by certain amount at the same
rate of
interest for 6 years and that for 9 years? [A]. 1 : 3 [B]. 1 : 4 [C]. 2 : 3 [D]. Data
inadequate [E]. None of these
Answer: Option C
Explanation:
Let the principal be P and rate of interest be R%.
Required ratio =
P x R x 6 100 = 6PR 6 P x R x 9
100 = = 2 : 3. 9PR 9 Or Assume the amount=100
If interest is 10% ,amount of interest is 10 rs.
then the amount of interest for 6 yrs = 6*10 rs = 60 rs
and for 9 yrs amt of interest for 9 years = 9*10 rs = 90rs
For ratio, s1/s2 = 60/90 = 2/3.
13. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest
been 2%
more, how much more interest would it have earned? [A]. Rs. 35 [B]. Rs. 245 [C].
Rs. 350 [D]. Cannot be determined [E]. None of these
Answer: Option D
Explanation:
We need to know the S.I., principal and time to find the rate.
Since the principal is not given, so data is inadequate.
1750 = PR7/100.
=>PR = 25000-----(1).
Again, SI = (P*102/100*R*7) / 100.
=>PR = (100*100*SI) / 7*102------(2).
By equating (1) and (2).
SI = 1785.
So ans is 1785-1750 = 35.
Or Let the rate of S.I is 100 (initially).
In the first case:
Sum = (S.I x 100)/(Rate of interest x time).
So sum = (1750 x 100)/(100 x 7) = 250.
In the 2nd case:
The interest rate is 2% more, so the interest rate is 102%.
S.I = (sum x time x Rate of interest)/100.
= (250 x 7 x 102)/100 = 1785.
So the gain in S.I is (1785-1750) = 35.
14. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He
immediately lends it
to another person at 6 p.a for 2 years. Find his gain in the transaction per year. [A].
Rs. 112.50 [B]. Rs. 125 [C]. Rs. 150 [D]. Rs. 167.50
Answer: Option A
Explanation:
Gain in 2 years = Rs. 5000 x 25 x 2 - 5000 x 4 x 2
4 100 100 = Rs. (625 - 400) = Rs. 225. Gain in 1 year = Rs. 225 = Rs. 112.50 2
----> 5000*4%
= 200.

----> 5000*6.25% =
312.50.
----> 312.50-200 =
112.50.

Answer :
112.50.

PTR/100 = 815
P*3*R/100 = 815
R/100=854- 815 p *
3 * 39 = 815 P * 117
= 815 p = 815-117 =
698 Or According to the
question,

SI + P = 815 in three
years and SI + P = 854
in four years

so 815 - P =
SI and 854 -
P = SI
Therefore,

815 - P = (P * 3 * R)/100 and -

--- eq 1 854 - P = (P * 4 *
R)/100 ---- eq 2 Now, eq 1 /
eq 2 gives

(815 - P)/(854 -
P) = 3/4 Solving
this eq, we get P
= 698

2. Mr. Thomas invested an amount of Rs. 13,900 divided in two different

schemes A and B at the simple interest rate of 14% p.a. and 11% p.a.
respectively. If the total amount of simple interest earned in 2 years be Rs. 3508,
what was the amount invested in Scheme B? [A]. Rs. 6400 [B]. Rs. 6500 [C]. Rs.
7200 [D]. Rs. 7500 [E]. None of these

Answer:
Option A