Aptitude

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

121. 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?

by
[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

122. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

by
[A]. 4 days
[B]. 6 days
[C]. 8 days
[D]. 12 days
✅ The correct answer is option C.
(A + B + C)’s 1 day’s work =
1
;

6

(A + B)’s 1 day’s work =
1
;

8

(B + C)’s 1 day’s work =
1
.

12

(A + C)’s 1 day’s work

=

2 x
1

–

1
+
1

6
8
12

=

1
–
5

3
24

=
3

24

=
1
.

8

So, A and C together will do the work in 8 days.

123. 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?

by
[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

124. A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

by
[A]. 5
[B].5 1 2
[C]. 6
[D]. 8
✅ The correct answer is option C.
B’s 10 day’s work =

1
x 10

=
2
.

15
3

Remaining work =

1 –
2

=
1
.

3
3

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

18

1
work is done by A in

18 x
1

= 6 days.

3
3

125. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

by
[A]. 4 days
[B]. 6 days
[C]. 8 days
[D]. 12 days
✅ The correct answer is option B.
Suppose A, B and C take x,
x
and
x
days respectively to finish the work.

2
3

Then,

1
+
2
+
3

=
1

x
x
x
2

6
=
1

x
2

x = 12.
So, B takes (12/2) = 6 days to finish the work.

126. A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?

by
[A]. 40
[B]. 50
[C]. 54
[D]. 60
✅ The correct answer is option D.
(A + B)’s 20 day’s work =

1
x 20

=
2
.

30
3

Remaining work =

1 –
2

=
1
.

3
3

Now,
1
work is done by A in 20 days.

3

Therefore, the whole work will be done by A in (20 x 3) = 60 days.

127. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:

by
[A]. 15 days
[B]. 20 days
[C]. 25 days
[D]. 30 days
✅ The correct answer is option C.
(A + B)’s 1 day’s work =
1

10

C’s 1 day’s work =
1

50

(A + B + C)’s 1 day’s work =

1
+
1

=
6
=
3
. …. (i)

10
50
50
25

A’s 1 day’s work = (B + C)’s 1 day’s work …. (ii)

From (i) and (ii), we get: 2 x (A’s 1 day’s work) =
3

25

A’s 1 day’s work =
3
.

50

B’s 1 day’s work

1
–
3

=
2
=
1
.

10
50
50
25

So, B alone could do the work in 25 days.

128. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

by
[A].13 1 days 3
[B]. 15 days
[C]. 20 days
[D]. 26 days
✅ The correct answer is option A.
Work done by X in 8 days =

1
x 8

=
1
.

40
5

Remaining work =

1 –
1

=
4
.

5
5

Now,
4
work is done by Y in 16 days.

5

Whole work will be done by Y in

16 x
5

= 20 days.

4

X’s 1 day’s work =
1
, Y’s 1 day’s work =
1
.

40
20

(X + Y)’s 1 day’s work =

1
+
1

=
3
.

40
20
40

Hence, X and Y will together complete the work in

40

= 13
1
days.

3
3

129. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?

by
[A]. 11:30 A.M.
[B]. 12 noon
[C]. 12:30 P.M.
[D]. 1:00 P.M.
✅ The correct answer is option D.
(P + Q + R)’s 1 hour’s work =

1
+
1
+
1

=
37
.

8
10
12
120

Work done by P, Q and R in 2 hours =

37
x 2

=
37
.

120
60

Remaining work =

1 –
37

=
23
.

60
60

(Q + R)’s 1 hour’s work =

1
+
1

=
11
.

10
12
60

Now,
11
work is done by Q and R in 1 hour.

60

So,
23
work will be done by Q and R in

60
x
23

=
23
hours 2 hours.

60
11
60
11

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

130. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

by
[A]. 8 hours
[B]. 10 hours
[C]. 12 hours
[D]. 24 hours
✅ The correct answer is option C.
A’s 1 hour’s work =
1
;

4

(B + C)’s 1 hour’s work =
1
;

3

(A + C)’s 1 hour’s work =
1
.

2

(A + B + C)’s 1 hour’s work =

1
+
1

=
7
.

4
3
12

B’s 1 hour’s work =

7
–
1

=
1
.

12
2
12

B alone will take 12 hours to do the work.