Quantitative Aptitude
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14.TIME AND WORK
Work
Work to be done is generally considered as one unit. It may be digging a trench, constructing
or Painting a wall, filling up or emptying a tank, reservoir or a cistern.
General rules to be followed in the problems on Time and Work
1. If A can do a piece of work in n days, then work done by A in 1 day is 1/n.
i.e. if a person can do some work in 12 days, he does 1/ 12th of the work in one day.
2. If As 1 days work =1/n , then A can finish the whole work in n days.
i.e. if a persons one days work is 1/10, then he can finish the whole work in 10 days.
3. If A is thrice as good a workman as B, then ratio of work done by A and B = 3 : 1. i.e. if a man
works three times as fast as a woman does, then when the work is complete,
3 parts of
the work has been done by the man and 1 part by the woman.
4. If A is thrice as good a workman as B, then ratio of time taken by A and B = 1 : 3. i.e. if the
woman takes 15 days to complete the work, then the man takes 5 days to complete the same work.
5. If two persons A and B can individually do some work in a and b days respectively, then A and B
together can complete the same work in ab/(a + b) days.
6. The fundamental rules on variation also apply in Time and Work.
(i) Work and men are directly proportional to each other i.e. if the work increases, the no. of men
required to do it, also increases, if the work is to be completed in the same number of days.
(ii) Men and days are inversely proportional, i.e. if the number of men increases, the number of days
required to complete the same work decreases and vice versa.
(iii) Work and days are directly proportional, i.e. if the work increases, the number of days required
also increases, if the work is to be completed with the same number of men and vice versa.
Example 1: Ravi can do a job 10 days. Determine his one day job.
Solution: Ravis 10 days work = 1
Ravis 1 day work =
Example 2: Tuktuki and Rasmani can do a job alone in 20 days and 30 days respectively. In how
many days the job will be finished, if they work together.
Solution: Tuktukis 1 day work =
Rasmanis 1 day work =
(Tuktuki + Rasmam)s 1 day work =
(Tuktuki + Rasmani) will complete the job in 12 days.
=12
Alternate: Required no. of days =
Example 3: Mary and Maurice can do a piece of work in 10 days and 15 days respectively. They
work together for 3 days and then Maurice leaves. Mary finishes the remaining work alone. In how
many days is the total work finished?
Solution . (Mary + Maurice)s 1 day work =
(Mary + Maurice)s 3 day work = =
Remaining work = =
Mary does this piece of work in = 10 days
Mary does the 1/2 piece of work in = 10 = 5 days
Hence, total number of days to finish the work = 3 + 5 = 8 days
Example 4: Ravi and Rishi can do a piece of work in 24 days, Rishi and Ronit in 30 days, Ronit and
Ravi in 40 days. In how many days will they finish it together and separately?
Solution: (Ravi and Rishi)s 1 days work =1/24
(Rishi and Ronit)s 1 days work = 1/30
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(Ronit and Ravi)s 1 days work = 1/40
On adding, we get
2 (Ravi + Rishi + Ronit)s 1 days work = (1/24 + 1/30 + 1/40) = 1/10
So,(Ravi + Rishi + Ronit)s 1 days work = 1/20
So, they all together can finish the work in 20 days.
Ravis 1 days work = [(Ravi + Rishi + Ronit)s 1 days work] - [(Rishi + Ronit)s 1 days work] =
(1/20 -1/30 ) = 1/60
So, Ravi alone can finish the work in 60 days.
Similarly, Rishis 1 day work = (1/20 - 1/40) = 1/40
So, Rishi alone can finish the work in 40 days
And Ronits 1 day work = (1/20- 1/24) = 1/120
So, Rishi alone can finish the work in 120 days.
Example 5: 4 men and 5 women do a piece of work in 8 days while 5 men and 5 women finish it in
6 days, 3 men and 5 women will finish it in how many days?
Solution: (4 men + 5 women)s 1 days work = 1 / 8
(5 men + 5 women)s 1 days work 1/6
Subtracting, 1 mans 1 days work = (1/6 - 1/8) = 1/24
(3 men + 5 women)s 1 days works = (1/8 - 1/24) = 1/12
Thus, 3 men and 5 women will finish it in 12 days.
EXERCISE
Directions (1-5): A can do a piece of work
in 8 days and B in 12 days. Find how much
time they will take to complete the work
under the following condition.
1. Working together
(a) 4 days
(b) 4 days
(d) 4 days
(c) 4 days
2. Working alternately starting with A
(a) 8 days
(b)8 days
(c) 9 days
(d) 9 days
3. Working alternately starting with B
(a) 8 days
(b) 8 days
(c) 9 days
(d) 9 days
4. If B leaves 3 days before the actual
completion of the work
(a) 2 days
(b) 3 days
(c) 6 days
(d) 9 days
5.
If B leaves 3 days before the scheduled
completion of the work
(a) 3 days
(b) 6 days
(c) 3 days
(d) 6 days
6. A and B together can complete a piece of
work in 35 days while A alone can
complete the same work in 60 days. In
how many days, B alone will be able to
complete the same work?
(a) 80 days
(b) 84 days
(c) 88 days
(d) 92 days
7. A and B can do a piece of work in 12
days, B and C can do it in 15 days and C
and A can do the same work in 20 days.
Find the number of days in which A
alone can do the same job.
(a) 20 days
(b) 30 days
(c) 45 days
(d) 60 days
8. A can do a piece of work in 15 days and
B alone can do it in 10 days. B works at it
for 5 days and then leaves. In how many
days, A alone can finish the remaining
work?
(a) 7 days
(b) 7 days
(c) 8 days
(d) 8 days
9. A and B can do a piece of work
separately in 8 and 12 h. If they work
alternate hours, A starting when will the
work be finished?
(b) 9 h
(a) 9 h
(c) 8 h
(d) 8 h
10. Two friends A and B working together
completed a work in 26 days. Their skills
of doing the work is in the ratio 8: 5.
How many days will B take, if engaged
alone?
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(a) 67 days
(b) 62 days
(c) 67 days
(d) 65 days
11. A and B together can do a piece of work
in 12 days, which B and C together can
do in 16 days. After A has been working
at it for 5 days and B for 7 days, C
finishes it in 13 days. In how many days
C alone will do the work?
(a) 16
(b) 24
(c) 37
(d) 48
12. A and B can do a piece of work in 45
days and 40 days respectively. They
bE.g.an to do the work together but A
leaves after some days and then B
completed the remaining work in 23
days. The number of days after which A
left the work was:
(a) 11
(b) 7
(c) 9
(d) 12
13. A can do a piece of work in 14 days
which B can do in 21 days. They bE.g.in
together but 3days before the completion
of the work, A leaves off. The total
number of days to complete the work is:
(a)
(b) 8
(c)
(d) 13
14. A, B and C can complete a work
separately in 24, 36 and 48 days
respectively. They started together but C
left after 4 days of start and A left 3 days
before the completion of the work. In
how many days will the work be
completed?
(a) 15 days
(b) 24 days
(c) 25 days
(d) 38 days
15. A, B and C together earn Rs. 300 per day,
while A and C together earn Rs.188 and
B and C together earn Rs.152. The daily
earning of C is:
(a) Rs.40
(b) Rs. 70
(c) Rs. 112
(d) Rs. 160
16. A, B and C are employed to do a piece of
work for Rs. 529. A and B together are
supposed to do of the work and B and
C together of the work. What amount
should A be paid?
(a) Rs. 320
(b) Rs. 345
(c) Rs. 355
(d) Rs.380
17. 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.450
(b) Rs.400
(c) Rs.600
(d) Rs.900
18. A sum of money is sufficient to pay As
wages for 21 days and B s wages for 28
days. The same money is sufficient to
pay the wages of both for:
(a) 12 days
(b) 12 days
(c) 16 days
(d) 24 days
19. 12 men can complete a piece of work in
4 days, while 15 women can complete
the same work in 4 days. 6 men start
working on the job and after working for
2 days, all of them stopped working.
How many women should be put on the
job to complete the remaining work, if it
is to be completed in 3 days?
(a) 15
(b) 19
(c) 23
(d) data inadequate
20. Sixteen men can complete a work in
twelve days. Twenty-four children can
complete the same work in eighteen
days. Twelve men and eight children
started working and after eight days three
more children joined them. How many
days will they now take to complete the
remaining work?
(a) 5 days
(b) 4 days
(c) 10 days
(d) 9 days
21. 5 men and 2 boys working together can
do four times as much work as a man and
a boy. Working capacities of a man and a
boy are in the ratio:
(a) 1 :2
(b) 2 : 1
(c) 1: 3
(d) 6 : 7
22. A and B can complete a piece of work in
80 and 120 days respectively. They
together start the work but A left after 20
days. After another 12 days C joined B
and now they complete the work in 28
more days. In how many days C can
complete the work, working alone?
(a) 100 days
(b) 112 days
(c) 120 days
(d) 126 days
23. 8 men and 10 women are working
together on a job and can complete it in
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and one model C tractor take 3 days to do
this job. Three tractors on each of models
A, B and C take 4 days to do the same
task. How long will it take to do the job
if a team is made up of four tractors of
different models?
(a) days
(b) days
10 days. The work done by each woman
is four-fifth of the work by each man. In
how many days 10 men alone complete
the same work?
(a) 20 days
(b) 12 days
(c) 15 days
(d) 16 days
24. There are 2 machine tools. The capacity
of the 1st machine tool is 20% less than
the 2nd one. The 1st machine tool
operated for 5 h whereas the 2nd one
operated for 4 h and together they
machined 3000 work pieces. The number
of work pieces machined by the 1st
machine is
(a) 950
(b) 1000
(c) 1032
(d) 1050
25. A firm has tractors of four models A, B,
C and D. Four tractors (two of model B
and one each of models C and D) plough
a field in 2 days. Two model A tractors
1
2
3
4
5
6
b
d
c
c
d
b
7
8
9
10
11
12
(c) days
(d) days
26. The efficiency of Ronil is twice that of
Sanjay and he can finish a work in 4 h
less than the time taken by Sanjay. If
both of them work together they can
finish the same work in
(a) 8 h
(b) 3 h
(c) 8/3 h
(d) 4/3 h
Answer Key
13
c
14
a
15
a
16
b
17
b
18
a
b
b
a
a
b
c
19
20
21
22
23
24
a
b
b
b
d
b
25
26
d
c
SOLUTIONS
1.
As one day work =
Bs one day work =
!
!
!
day
"
days
"
2. Work done in first 2 days
!
!
"
=
$
!
Work done in first 8 days
"
=
Remaining work =
"
Required number of days =
So, total required time =
(A + B)s one day work =
$
$
!
!
!
(
Work done by A in 9th day =
$
After 9 days, the remaining work has
!
!
!
to be done
(
$
In the 10th day B will come to do the
work and he will complete all the
remaining work. Time taken by B for it
days
3. Here, there will be no difference in work
completed by the 8th day.
On the 9th day B works alone and does
!
of the work
!
So, after 9 days remaining work to be done
"
!
!!
!
(
!
!
!
Time taken by A to do the remaining work
!
days
!
So, total required time =8+1+ =9
4. If B leaves 3 days before the actual
completion of the work, then A will work
alone for the last 3 days.
So, in last 3 days work done by A =
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"
A and B have done
of the work
$
$
Time taken by A and B together to do 5/8 of
"
! '$
the work =
= 3 days
$
! #$
Total required time = 3 + 3 = 6 days
5. Time taken by A and B working together to
finish the work = days
"
Bs work of 3 days =
!
Since, B leaves 3 days before the
scheduled completion of the work. So, this
!
work
be done by
A. So, time taken to finish 1/4 of the work
by
!
A = = 2 days
Total required time
! ! ! & "
!
= =
6. Bs one day work = - =
" ( ( $
Required number of days =84
!
7. Work done by A and B in one day=
!
Work done by B and C in one day =
!"
!
Work done by C and A in one day =
Adding all these, 2 (A + B + C)s work of
!
!
!
!
one day =
!
!"
"
(4 + B + C)s one day work =
!
As one day work = (A + B + C)s one
day work - (B + C)s one day work
As one day work
!
Hence, A can do this work in 30 days.
! !
8. Work done by B in 5 days =5* =
!
!
Remaining work=1-
Time taken by A to finish the remaining
!
!
work= "
9.
(A + B)s 2 h work =
(A + B)s 8 h work =
$
!
"'
"
Work done by A in 9th h =
"
"
(
!
$
Total work done up to 9 h = =
th
Remaining work =
Bs 1 h work =
B can do
!
of the work in
!
!
Both can finish the job in
10. Skill ratio of A and B = 8 : 5
"
11. As 5 days work + Bs 7 days work + Cs
13 days work = 1
(A + B)s 5 days work + (B + C)s
2 days work + Cs 11 days work = 1
"
Cs 11 days work = 1
!
!(
Cs 11 days work
"
!!
=
!
!(
!!
Cs 1 days work =
!!
C alone can finish the work in 24 days.
12. (A + B)s 1 days work
!
!
!&
=
"
(
Work done by B in 23 days
!
=
!
!&
Remaining work =
Time taken by A and B to finish the
(
!&
remaining work=
!&
A left after 9 days.
!
!
13. Bs 3 days work
!
!
&
Remaining work =
&
&
(A + B)s 1 days work
# $
(
work is done by A and B in
&
!
# $
"
(
Hence, total time taken =
! days
"
= 10 days.
"
14. (A+ B + C) s 1 days work
!
$
#
!
Work done by (A + B + C) in 4 days
!
!
=
!
(
Work done by B in 3 days
!
!
=
!
(
"
Work done by B is of the whole which
!
he does in 26 days
Number of days taken by B to do the
('!
whole work
= 67 days
!
"
Remaining work = %
&
(
!
%
(A + B)s 1 days work
# $
!
"
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Time taken by A and B to finish 5/9th of
" &
the work= ' =8 days
%
"
Hence, total time taken = (4+ 3+8) days =
15days.
15. Bs daily earning = Rs. (300 - 188)
= Rs.112.
= Rs. [152 - 11)]= Rs.40.
$
!"
16. Work done by A =
A : (B +C) =
!"
$
= 15 : 8
So, As share =Rs.
!
!"
= Rs. 345.
!
17. Cs l days work =
(
$
"
!
As wages : Bs wages : Cs wages
: :
: !:
!
Cs share = Rs.
!
= Rs. 400.
$
18. Let total money be Rs. x.
)
As 1 days wages = Rs.
!
)
B s 1 days wages = Rs.
$
(A + B)s 1 days wages
)
)
)
= Rs.
= Rs.
!
Money is sufficient to pay the wages of
both for 12 days.
!
19. 1 man 1 days work ;
$
1 woman 1 days work=
(
6 mens 2 days work =
!
Remaining work =
!
$
!
Now,
work is done in 1 day by 1
(
woman.
So, work will be done in 3 days by
!
!%
1 childs 1 days Work=
;
!
Work done in 8 days =
!(
!
"
"
"
!%
"
$
!%
"
!(
work will be done by them in
!%
= 4 days.
!%
"
21. Let 1 mans 1 days work = x and 1 boys 1
days work = y.
Then,
5x + 2y = 4 (x + y)
x =2y
)
22. A did the work for 20 days, B did the work
for (20 + 12 + 38) = 60 days, C did the
work for 28 days.
Let C alone can complete the work in x
days.
Fraction of work did by A + Fraction of
work did by B + Fraction of work did by C
=1
(
$
Or
$
!
)
Or )
= 112 days
C alone can complete the work in 112 days
23. 1 Woman = men
"
8 Men + 10 Women
= 8 Men + 10 Men = 16 Men
"
16 Men can complete the work in 10 days.
10 Men can complete the work in
= 16 days
24. Let the capacity of the second machine be
x work pieces per hour.
Capacity of the 1st machine tool
= 0.8 x.
* . ), )
)
)
Number of work machined by the first
Tool = 5 0.8 x = 1000
!
!
!
25. .(i)
*
= 15 women.
20. 1 mans 1 days work =
!%
Remaining work =
"
"
(12 men + 11 children)s 1 days work
#
$
!
!%
work is done by them in 1
Now,
!(
day.
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+
!
,
!
!
(ii)
!
and ...(iii)
*
+
Subtracting Eq. (i) from Eq. (ii), we
!
!
get ...(iv)
*
,
(
Subtracting Eq. (iii) from Eq. (ii), we
get
- .
!
..(v)
*
(
Subtracting Eq. (v) from Eq. (iv), we
get
!
!
.............(vi)
,
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Adding Eqs. (iii) and (iv), we get
"
- . / 0 !
!
Hence, A, B, C and D will take days to
&
do the required job.
26. As the efficiency of Ronil is twice that of
Sanjay, Ronil will take hours for
completion of the work, when Sanjay is
taking 2x h.
Given, 2x x= 4=> x= 4
!
$
Hence, they take h
#
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