STD and Trains
1) Ravi travelled 1200 km by air which formed (2/5) of his trip. One third of the whole trip, he
travelled by car and the rest of the journey he performed by train. The distance travelled
by train was :
a. 1600 km
b. 800 km
c. 1800 km
d. 480 km
2) What is the average speed if a person travels from A to B and then B to C at the speeds
of 10 km/hr and 20 km/hr, respectively for equal intervals of time?
a. 15 kmph
b. 13.33 kmph
c. 12 kmph
d. 11.11 kmph
3) What is the average speed if a person travels from A to B and back at the speeds of 10
km/hr and 20 km/hr, respectively?
a. 15 kmph
b. 13.33 kmph
c. 12 kmph
d. 11.11 kmph
4) A car covers four successive three km stretches at speeds of 10 km/hr, 20 km/hr, 30
km/hr and 60 km/hr respectively. Its average speed over this distance :
a. 10 km/hr
b. 20 km/hr
c. 30 km/hr
d. 25 km/hr
5) A train covers a distance in 50 minutes. If it runs at a speed of 48 km per hour on an
average, the speed at which the train must run to reduce the time of journey to 40
minutes will be :
a. 50 km/hr
b. 55 km/hr
c. 60 km/hr
d. 70 km/hr
6) A man goes uphill with an average speed of 35 km/hr and comes down with an average
speed of 45 km/hr. The distance travelled in both the cases being the same, the average
speed for the entire journey is :
a. 38 3/8 km/hr
b. 39 3/8 km/hr
c. 40 km/hr
d. None of these
7) P and Q are two stations. A train goes from P to Q at 64 km/hr and returns to P at a
slower speed. If its average speed for the whole journey is 56 km/hr, at what speed did it
return?
a. 48 km/hr
b. 49.77 km/hr
c. 52 km/hr
d. 47 km/hr
8) Two men A and B walk from P to Q, a distance of 21 km at 3 km/h and 4 km/h
respectively. B reaches at point Q and returns immediately and he meets A at point R.
Find the distance from P to R.
a. 15 km
b. 18 km
c. 20 km
d. 24 km
9) Buses take 12 hr to cover the distance of 120 km between A and B. A bus starts from
point A at 8.00 a.m. and another bus starts from point B at 10.00 a.m. on the same day.
When do the two buses meet?
a. 2 pm
b. 3 pm
c. 4 pm
d. 5 pm
10) Ravi started cycling along the boundaries of a square field from corner point A. After half
an hour, he reached the corner point C, diagonally opposite to A. If his speed was 8
km/hr. what is the area of the field in square km ?
a. 4
b. 8
c. 64
d. Cannot be determined
11) A man walking at 3 km/hr crosses a square field diagonally in 2 min. The area of the field
is :
a. 2500 m2
b. 3000 m2
c. 5000 m2
d. 6000 m2
12) A cart has to cover a distance of 80 km in 10 hours. If it covers half of the journey in
(3/5)th time, what should be its speed to cover the remaining distance in the time left?
a. 8 km/hr
b. 20 km/hr
c. 6.4 km/hr
d. 10 km/hr.
13) The ratio between the rates of walking of P and Q is 2 : 3. If the time taken by Q to cover
a certain distance is 36 minutes, the time taken by P to cover that much distance is :
a. 24 min
b. 54 min
c. 48 min
d. 21.6 min
14) A train travelling at 36 kmph completely crosses another train having half its length and
travelling in the opposite direction at 54 kmph, in 12 seconds. If it also passes a railway
platform in 112 minutes, the length of the platform is :
a. 560 metres
b. 620 metres
c. 700 meres
d. 750 metres
15) A train 100 metres in length passes a milestone in 10 seconds and another train of the
same length travelling in opposite direction in 8 seconds. The speed of the second train
is :
a. 36 kmph
b. 48 kmph
c. 54 kmph
d. 60 kmph
16) Two trains are running in opposite directions with speed of 62 kmph and 40 kmph
respectively. If the length of one train is 250 metres and they cross each other in 18
seconds, the length of the other train is :
a. 145 metres
b. 230 metres
c. 260 metres
d. Cannot be determined
17) A train 100 metres long moving at a speed of 50 kmph crosses a train 120 metres long
coming from opposite direction in 6 seconds. The speed of second train is :
a. 132 kmph
b. 82 kmph
c. 60 kmph
d. 50 kmph
18) Two stations A and B are 110 kms.apart on a straight line. One train starts from A at 7
a.m and travels towards B at 20 km per hour speed. Another train starts from B at 8.a.m
and travels towards A at a speed of 25 km per hour. At what time will they meet?
a. 9 a.m
b. 10 a.m
c. 11 a.m
d. None of these.
19) 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. 72 metres
b. 54 metres
c. 50 metres
d. 45 metres
20) A man standing on a railway platform notices that a train going in one direction takes 10
seconds to pass him and other train of the same length takes 15 seconds to pass him.
Find the time taken by the two trains to cross each other when they are running in the
opposite directions.
a. 12
b. 14
c. 18
d. 25
21) A man standing on a railway platform notices that a train going in one direction takes 9
seconds to pass him and other train of the same length takes 6 seconds to pass him.
Find the time taken by the two trains to cross each other when they are running in the
same direction.
a. 15
b. 30
c. 32
d. 36
22) A train moving at the rate of 36 km per hour crosses a standing man in 10 seconds. It will
cross a platform 55 metres long in :
a. 5 1/2 seconds
b. 6 seconds
c. 7 1/2 seconds
d. 15 1/2 seconds
23) A train of length 150 metres take 10 seconds to pass over another train 100 metres long
coming from the opposite direction. If the speed of the first train is 30 kmph, the speed of
the second train is :
a. 54 kmph
b. 60 kmph
c. 72 kmph
d. 36 kmph
24) A 150 meter long train crosses a man walking at the speed of 6 kmph in the opposite
direction in 6 seconds. The speed of the train in km/hr is :
a. 66
b. 84
c. 96
d. 106
25) A train speeds past a pole in 15 seconds and speeds past a platform 100 meters long in
25 seconds. Its length in meters is :
a. 200
b. 150
c. 50
d. Data inadequate
Solutions:
1) Let the total distance be x km.
Then, 2/5 x=1200⇒x=1200×5/2=3000
Distance travelled by car = (1/3×3000) = 1000 km
Distance travelled by train = [(3000-(1200+1000)] km = 800 km
2)
The average speed = (10+20)2=15km/ℎ
3) In this case, times are not given.
General formula for Average speed = Distance/Total Time
Let the total distance = 2D.
Total time taken = T = (D/10)+(D/20)
So, Average speed = 2D/T=2D/(D/10+D/20)=2D/D(1/10+1/20)=13 1/3 km/hr
Alternative Method:
Use formula = 2xy/x+y
4) Total time taken = (3/10+3/20+3/30+3/60) hrs = 3/5 hrs
Average speed = {12/3/5} km/hr = (12×5/3) km/hr = 20 km/hr.
5) Distance = (48×50/60) km = 40 km
Required Speed = [40/(40/60)] km/hr = (40×60/40) km/hr=60 km/hr
6) Average speed = (2×35×45/(35+45)) km/hr = 39 3/8 km/hr.
7) Let the required speed be x km/hr.
Then, 2×64× y/64+y=56
⇒128y=64×56+56y
y = 64×56/72=49.77 km/hr
8) Both of them together have walked twice the distance from P to Q i.e. 42 km.
Ratio of speeds of A and B = 3 : 4.
Therefore, Distance travelled by A = PR = 3/7 x 42 = 18 km.
9) The distance between A and B is 120 km.
Speed of the buses = 120/12 = 10 km/hr
By 10.00 a.m., the bus from A would have covered 20 km.
Hence, the distance between the buses at 10.00 a.m. = 120 – 20 = 100 km
Relative speed of the buses = 20 km/hr.
Time taken to meet = 100/20 = 5 hr after B starts
i.e., the buses will meet at 3 p.m.
10) As his speed is 8kmph, in half an hour he covers 4 kmph.
4 km is equal to two sides of the square.
So side of the square = 2 km
Area of the field = a2 = 2 km x 2 km = 4 km
11) Speed in meters per second = (3×5/18) m/sec = (5/6) m/sec.
Distance covered in (2×60)sec. = (5/6×2×60)m = 100 m
Length of diagonal = 100 m
So, area = ½ ×(diagonal)2 = (1/2 ×100×100)m2 = 5000 m2
12) Distance left = (1/2 ×80) km = 40 km
Time left = (1−3/5)×10 = 2/5×10=4hrs
Speed required = (40÷4) km/hr = 10 km/hr.
13) We know that, ratio of times are inversely proportional to ratio of speeds.
Ratio of times taken = 1/2:1/3 = 3 : 2
let the time taken by P is x minutes.
∴ 3 : 2 = x : 36
⇒3/2=x/36
⇒ x = 54 min
14) Let the length of slower train be x metres and the length of faster train be (x/2) meters.
Relative speed = (36 + 54)km/hr =(90×5/18) m/sec = 25 m/sec
3x/2×25=12⇒3x=600⇒x=200 m
Length of slower train = 200 m
Let the length of platform be y metres
Then, 200+y/36+5/18=90⇒200×y=900 or
y = 700 m
Length of platform = 700 m
15) Speed of first train = (100/10) m/sec = 10 m/sec
Let the speed of 2nd rain be x m/sec
Relative speed = (10 + x) m/sec
200/10+x=8⇒200=80+8x⇒x=15
Speed of 2nd train = 15 m/sec = (15×18/5) km/hr = 54 km/hr.
16) Let the length of the another train = x meres
Their relative speed = (62 + 40) km/hr = (102×5/18)m/sec = (85/3)
(250+x)/85/3=18⇒3(250+x)/85=18
⇒250+x=510⇒x=260
Length of another train = 260 m
17) Let the speed of the second train be x km/hr.
Relative speed = (50 + x) km/hr = [(50+x)×5/18] m/sec =(250+5x/18) m/sec.
⇒(100+120)/(250+5x/18)=6 or
220×18=6(250+5x) or 30x = 3960-1500 or x = 246030=82
Speed of the second train = 82 m/s.
18) Suppose they meet x hrs after 7 a.m.
Distance covered by A in x hrs = (20×x) km
Distance covered by B in (x - 1) hrs = 25(x - 1) km
20x + 25(x - 1)=110 or
45x = 135 or x = 3
So, they meet at 10 a.m
19) Let the length of the train be x km and its speed y km/hr. Then, speed relative to first man
= (y−2) km/hr.
Speed relative to second man = (y−4) km/hr.
x/y−2=9/60×60 and x/y−4=10/60×60
9y−18=3600x or 10y−40=3600x
So, 9y−18=10y−40 or y=22
x/22−2=9/3600 or x = 20×9/3600=1/20
= (1/20×1000)m = 50 m
20) Time taken for the trains to cross each other = 2ab/a+b=2×10×15/25 = 12 seconds
21) Time taken for the trains to cross each other = 2ab/a−b=2×9×6/3 = 36 seconds
22) Speed = (36×5/18) m/sec = 10 m/sec
Let the length of the train be x metres
Then, x/10=10⇒x=100 m.
Time taken to cross the platform = (100+55/10) sec = 15 1/2 sec
23) Relative speed = 150+100/10=25 m/s = (25×18/5) km/hr = 90 km/hr
Speed of second train = (90 - 30) km/hr = 60 km/hr
24) Let the speed of the train be x km/hr
Relative speed = (x + 6) km/hr = [(x+6)×518] m/sec
150/6=(x+6)×5/18
⇒ 5x + 30 = 450 (or) x = 84 km/hr
25) Let the length of the train be x metres and its speed be y meters/sec.
Then, x/y=15⇒y=x/15
Now, x+100/25=x/15⇒x=150 m
