Time and Work

21. 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
✅ The correct answer is option B.
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.

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
✅ The correct answer is option C.
(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.

23. 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
✅ The correct answer is option B.
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

24. 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
✅ The correct answer is option A.
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
200

(15 men + 20 boy)’s 1 day’s work =

15
+
20

=
1
.

100
200
4

15 men and 20 boys can do the work in 4 days.

26. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

[A]. 23 days
[B]. 37 days
[C]. 37
[D]. 40 days
✅ The correct answer is option C.
Whole work is done by A in

20 x
5

= 25 days.

4

Now,

1 –
4

i.e.,
1
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

28. 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
✅ The correct answer is option A.
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
.

96
80

(P + Q)’s 1 hour’s work =

1
+
1

=
11
.

96
80
480

So, both P and Q will finish the work in

480

hrs.

11

Number of days of 8 hours each =

480
x
1

=
60
days = 5
5
days.

11
8
11
11

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