Time and Work

2. 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:

[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.

3. 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?

[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

4. 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 ?

[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.

6. 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 :

[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.

7. 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?

[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

8. 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?

[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.

9. 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:

[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

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