Aptitude

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📘 Height-and-Distance
📘 series
📘 Time and Distance
📘 Time and Work
📘 Train

131. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

by
[A]. 4 days
[B]. 6 days
[C]. 8 days
[D]. 18 days
✅ The correct answer is option A.
Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.

B’s 1 day’s work =
1
.

12

A’s 1 day’s work =
1
; (2 times of B’s work)

6

(A + B)’s 1 day’s work =

1
+
1

=
3
=
1
.

6
12
12
4

So, A and B together can finish the work in 4 days.

132. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

by
[A]. 18 days
[B]. 24 days
[C]. 30 days
[D]. 36 days
✅ The correct answer is option A.
2(A + B + C)’s 1 day’s work =

1
+
1
+
1

=
15
=
1
.

30
24
20
120
8

Therefore, (A + B + C)’s 1 day’s work =
1
=
1
.

2 x 8
16

Work done by A, B, C in 10 days =
10
=
5
.

16
8

Remaining work =

1 –
5

=
3
.

8
8

A’s 1 day’s work =

1
–
1

=
1
.

16
24
48

Now,
1
work is done by A in 1 day.

48

So,
3
work will be done by A in

48 x
3

= 18 days.

8
8

133. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

by
[A]. 30 days
[B]. 40 days
[C]. 60 days
[D]. 70 days
✅ The correct answer is option C.
Let A’s 1 day’s work = x and B’s 1 day’s work = y.

Then, x + y =
1
and 16x + 44y = 1.

30

Solving these two equations, we get: x =
1
and y =
1

60
60

B’s 1 day’s work =
1
.

60

Hence, B alone shall finish the whole work in 60 days.

134. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

by
[A]. 1 day 24
[B]. 7 day 24
[C]. 3 3 days 7
[D]. 4 days
✅ The correct answer is option C.
Formula: If A can do a piece of work in n days, then A’s 1 day’s work =
1
.

n

(A + B + C)’s 1 day’s work =

1
+
1
+
1

=
7
.

24
6
12
24

Formula: If A’s 1 day’s work =
1
,
then A can finish the work in n days.

n

So, all the three together will complete the job in

24
days
=

3
3
days.

7
7

135. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

by
[A]. 15
[B]. 16
[C]. 18
[D]. 25
✅ The correct answer is option B.
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.
Suppose Tanya takes x days to do the work.

5 : 4 :: 20 : x    x =

4 x 20

5

x = 16 days.
Hence, Tanya takes 16 days to complete the work.

136. 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