Time and Work

11. 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:

by
[A]. 5 days
[B]. 6 days
[C]. 10 days
[D]. 10 1 days 2
✅ The correct answer is option C.
(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.

12
12

12. 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?

by
[A]. 6 days
[B]. 10 days
[C]. 15 days
[D]. 20 days
✅ The correct answer is option B.
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.

13. 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?

by
[A]. 35
[B]. 40
[C]. 45
[D]. 50
✅ The correct answer is option B.
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.

14. 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 :

by
[A].9 1 days 3
[B]. 11 days
[C].12 1 days 4
[D].16 1 days 3
✅ The correct answer is option B.
(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

15. 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 :

by
[A]. 1 4
[B].1 10
[C].7 15
[D].8 15
✅ The correct answer is option D.
A’s 1 day’s work =
1
;

15

B’s 1 day’s work =
1
;

20

(A + B)’s 1 day’s work =

1
+
1

=
7
.

15
20
60

(A + B)’s 4 day’s work =

7
x 4

=
7
.

60
15

Therefore, Remaining work =

1 –
7

=
8
.

15
15

16. 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?

by
[A]. Rs. 375
[B]. Rs. 400
[C]. Rs. 600
[D]. Rs. 800
✅ The correct answer is option B.
C’s 1 day’s work =
1
–

1
+
1

=
1
–
7
=
1
.

3
6
8
3
24
24

A’s wages : B’s wages : C’s wages =
1
:
1
:
1
= 4 : 3 : 1.

6
8
24

C’s share (for 3 days) = Rs.

3 x
1
x 3200

= Rs. 400.

24

17. 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?

by
[A]. 3
[B]. 5
[C]. 7
[D]. Cannot be determined
✅ The correct answer is option C.
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.

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?

by
[A]. 7 hours 30 minutes
[B]. 8 hours
[C]. 8 hours 15 minutes
[D]. 8 hours 25 minutes
✅ The correct answer is option C.
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

40

= 8
1
hours (or) 8 hours 15 minutes.

4

19. 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?

by
[A]. 3 : 4
[B]. 4 : 3
[C]. 5 : 3
[D]. Data inadequate
✅ The correct answer is option B.
(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)

20. 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:

by
[A].9 1 days 5
[B].9 2 days 5
[C].9 3 days 5
[D]. 10
✅ The correct answer is option C.
(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
48

So, C alone can do the work in
48
= 9
3
days.

5
5