Time and Work questions

CONCEPT TEST: Time & Work

  1. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
A.

1

4

B.

1

10

C.

7

15

D.

8

15

Answer: Option DExplanation:

A’s 1 day’s work =

1

;

15

 

B’s 1 day’s work =

1

;

20

 

(A + B)’s 1 day’s work =

1

+

1

=

7

.

15

20

60

 

(A + B)’s 4 day’s work =

7

x 4

=

7

.

60

15

 

Therefore, Remaining work =

1 –

7

=

8

.

15

15

 

  1. A can laid 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
Answer: Option CExplanation:

(A + B + C)’s 1 day’s work =

1

,

4

 

A’s 1 day’s work =

1

,

16

 

B’s 1 day’s work =

1

.

12

 

 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

  1.  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    ays
  1. 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

Answer: Option B

Explanation:

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.

24

  1. 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
  1. 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

Answer: Option A

Explanation:

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.

  1. 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

Answer: Option C

Explanation:

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

  1. 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.

Answer: Option D

Explanation:

(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.

 

  1. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
A. 35 B. 40
C. 45 D. 50
Answer: Option BExplanation:Let 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y.

Then, 4x + 6y =

1

and 3x + 7y =

1

.

8

10

 

Solving the two equations, we get: x =

11

y =

1

400

400

 

 1 woman’s 1 day’s work =

1

.

400

 

 10 women’s 1 day’s work =

1

x 10

=

1

.

400

40

Hence, 10 women will complete the work in 40 days.

  1. 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

Answer: Option A

Explanation:

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.

  1. 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

Answer: Option A

Explanation:

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.

  1. 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

Answer: Option C

Explanation:

(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.

  1. 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

Answer: Option B

Explanation:

(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)

 

  1. A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can be done by A alone in :
A.

9

1

days

3

B. 11 days
C.

12

1

days

4

D.

16

1

days

3

Answer: Option B

Explanation:

(A’s 1 day’s work) : (B’s 1 day’s work) =

7

: 1   =   7 : 4.

4

Let A’s and B’s 1 day’s work be 7x and 4x respectively.

Then, 7x + 4x =

1

         11x =

1

         x =

1

.

7

7

77

 

 A’s 1 day’s work =

1

x 7

=

1

.

77

11

  1. 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

Answer: Option A

Explanation:

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

 

  1. 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:
A. 4 days B. 6 days
C. 8 days D. 12 days

Answer: Option B

Explanation:

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.

  1. 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

Answer: Option C

Explanation:

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.

 

  1. 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

Answer: Option C

Explanation:

(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.

 

  1. 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:
A. 5 days B. 6 days
C. 10 days D.

10

1

days

2

Answer: Option C

Explanation:

(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.

 

 

 

 

 

 

 

 

  1. 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

Answer: Option A

Explanation:

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