Aptitude Archives

111. 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

✅ 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.

112. 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

✅ The correct answer is option C.
1 woman’s 1 day’s work =
1

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.

113. 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

✅ 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.

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

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

114. 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

✅ 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)

115. 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 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
,

A’s 1 day’s work =
1
,

B’s 1 day’s work =
1
.

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

116. 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
;

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.

117. 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.

2
work will be done by a in

15 x
2

= 10 days.

3
3

Hence, the total time taken = (10 + 2) = 12 days.

118. 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.

So, A takes 30 days to do the work.

A’s 1 day’s work =
1

B’s 1 day’s work =
1

(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

119. 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.

120. 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

✅ The correct answer is option B.
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
60
10

Work done in 3 days =

1
+
1

=
1
.

10
10
5

Now,
1
work is done in 3 days.

Whole work will be done in (3 x 5) = 15 days.