Time and Work :(96) MCQs with Answers

1.

If 8 men can dig a well in 18 days, then the number of days, 12 men will take to dig the same well will be

   A.) 12 days
   B.) 10 days
   C.) 8 days
   D.) 16 days

Answer: Option 'A'

Work done = 8 × 18 
Then, 8 × 18 = 12 × ? days 
? days = 8 × 18/12 = 12 days

2.

If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in 

   A.) 7 days
   B.) 6 days
   C.) 4 days
   D.) 3 days

Answer: Option 'D'

That is, 1 person can do one time of the work in 3 days. 
Therefore, 7 persons can do 7 times work in the same 3 days itself.

3.

A particular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to completed the job if the two teams work together? 

   A.) 4
   B.) 6
   C.) 18
   D.) 9

Answer: Option 'A'

Consider men’s work days as one group and women’s working days as other group Then, the required No. of days = 12 × 6/18 = 4 days.

4.

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 is: 

   A.) 4 days
   B.) 6 days
   C.) 8 days
   D.) 18 days

Answer: Option 'A'

That is, if b alone can finish the work in 12 days, 
A alone can finish the work in 6 days.
If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. 
A and B can together finish the work in 6 × 12/18 days = 4 days.

5.

8 children and 12 men complete a certain piece of work in 9 days. Each child takes twice the time taken by a man to finish the work. In how many days will 12 men finish the same work?

   A.) 8
   B.) 10
   C.) 12
   D.) 14

Answer: Option 'C'

8 children = 4men 
Then, 4 + 12 = 16 men completes the job in 9 days 
Then, 16 × 9 = 12 × ? days 
? days = 16 × 9/12 = 12 days.

6.

A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was: 

   A.) 6
   B.) 8
   C.) 9
   D.) 12

Answer: Option 'C'

A and B together can finish the work in 45 × 40/85 = 360/17 days 
A and B’s 1 day’s work = 17/360 
A’s 1 day’s work = 1/45 
B’s 1 day’s work = 1/40 
B’s 23 day’s work 1/40 × 23 = 23/40 
Remaining work = 1 – 23/40 = 17/40 
17/40 of the work is done by A and B together 
17/40 of the work is done by A and B together in = 17/40/17/360 = 17/40 × 360/17 days 
= 9 days
Therefore, A left after 9 days.

7.

A sum of money is sufficient to pay P’s wages for 25 days or Q’s wages for 30 days. The money is sufficient to pay the wages of both for 

   A.) 13 5/11 days
   B.) 13 days
   C.) 13 6/11 days
   D.) 13 7/11 days

Answer: Option 'D'

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. 
Here, wages can be taken as days, 
Then, 25 ×30/ 55 = 13 7/11 days.

8.

A and B can complete a given work by working together in 8 days. B takes twice the number of days to complete the work compared to A. In how many days A can finish the work by working alone? 

   A.) 16
   B.) 12
   C.) 14
   D.) 18

Answer: Option 'B'

Let the time taken by A to finish the work = x days
Then, time taken by B to finish the work = 2x days

Given, Time taken by A and B together ie., (A + B) = 8 days.
=>1/(A + B) = (1/A) + (1/B)
=> 1/8 = (1/x) + (1/2x)
=> 1/8 = (2 + 1) / 2x
=> 1/8 = 3/2x
Taking reciprocal on both sides,
=> 8 = 2x / 3
=> 8 * 3 = 2x
=> 24/ 2 = x
=>x = 12
A alone complete the work in 12 days.

9.

A and B can do a job together in 7 days. A is 1 ¾ times as efficient as B. the same job can be done by A alone in:

   A.) 9 1/3 days
   B.) 11 days
   C.) 12 ¼ days
   D.) 16 1/3 days

Answer: Option 'B'

1 ¾ = 7/4 
7/4 A = B, replacing B by 7/4 A, we get 
A × 7/4 A/ A + 7/4 A = 7days 
7 A × A/4 / 11A/4 = 7 A × A/ 11 A = 7A /11 = 7 
A = 77/7 = 11, So, A alone can finish the work in 11 days.

10.

A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field? 

   A.) 10 hours
   B.) 20 hours
   C.) 30 hours
   D.) 40 hours

Answer: Option 'C'

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days. 
Therefore, the No. of hours required by B = 10 × 15/ 15 – 10 = 150/5 = 30 hours.

11.

If 5 girls can embroider a dress in 9 days, then the number of days taken by 3 girls will be 

   A.) 20 days
   B.) 10 days
   C.) 14 days
   D.) 15 days

Answer: Option 'D'

That is, 5 × 9 = 3 × ? 
? = 5 × 9/3 = 15 days

12.

A work could be completed in 100 days. However, due to the absence of 10 workers, it was completed in 110 days then, the original number of workers was 

   A.) 100
   B.) 110
   C.) 55
   D.) 50

Answer: Option 'B'

Let ‘x’ be the original number of workers 
Then, x × 100 = ( x – 10) 110 
100 x = 110x – 1100 
1100 = 10 x 
x = 110.

13.

The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in the ratio: 

   A.) 3 : 4
   B.) 9 : 16
   C.) 4 : 3
   D.) 3 : 2

Answer: Option 'C'

The No. of days taken by them = inverse ratio = 4 : 3.

14.

Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is 

   A.) 15 days
   B.) 10 days
   C.) 9 days
   D.) 8 days

Answer: Option 'D'

If A can complete a work in x days and B can complete the same work in y days, then, both 
of them together can complete the work in x y/ x+ y days. 
That is, the required No. of days = 10 × 40/50 = 8 days.

15.

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.) 1/24 day
   B.) 7/24 day
   C.) 3 3/7 days
   D.) 4 days

Answer: Option 'C'

When A, B and C can do a work in x, y and z days respectively. Then, the three of them 
together can finish the work in xyz/ x y + y z + x z days
Therefore, the No. of days taken by them together = 24 × 6 × 12/24 × 6 + 6 × 12 + 24 × 12 
= 24 × 6 × 12/ 504 = 3 3/7 days.

16.

A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be 

   A.) 8 days
   B.) 6 days
   C.) 7 days
   D.) 5 days

Answer: Option 'A'

If A can complete a work in x days and B can complete the same work in y days, then, both 
of them together can complete the work in x y/ x+ y days 
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.

17.

30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers required to finish the same piece of work in 30 days will be 

   A.) 15 days
   B.) 21 days
   C.) 25 day
   D.) 22 day

Answer: Option 'B'

That is, 1 work done = 30 × 7 ×18 = ? × 6 × 30 
? (No. of labourers) = 30 × 7 × 18/6 × 30 = 21

18.

12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required

   A.) 4 days
   B.) 5 days
   C.) 6 days
   D.) 8 days

Answer: Option 'D'

That is, 1 work done = 12 × 8 × 10 
Then, 12 8 × 10 = ? × 15 × 8 
? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days.

19.

Adam can do a job in 15 days, John can do the same job in 20 days. If they work together for 4 days on this job. What fraction of job is incomplete?

   A.) (1 / 4)
   B.) (1 / 10)
   C.) (7 / 15)
   D.) (8 / 15)

Answer: Option 'D'

Adam can do 1/15 of the job per day
John can do 1/20 of the job per day
If they work together they can do 7/60 of the work together
Remaining job 1 - 4*7/60 = 32/60 = 8/15

20.

3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work? 

   A.) 4 days
   B.) 10 days
   C.) 15 days
   D.) 20 days

Answer: Option 'A'

3 men = 5 women 
1 woman = 3/5 men 
So, 5 women = 3/5 × 5 = 3 men 
6 men and 5 women = 6 + 3 = 9 men 
1 work done = 3 men × 12 days 
3 × 12 = 9 × ? days 
? days = 3 × 12/9 = 4 days.

21.

Tapas works twice as much as Mihir. If both of them finish the work in 12 days, Tapas alone can do it in: 

   A.) 20 days
   B.) 24 days
   C.) 18 days
   D.) 20 days

Answer: Option 'C'

Mihir = 2 Tapas (Consider, Tapas as ‘T’ and Mihir as “M”) 
So, T ×2 T/ T + 2T = 12 
2 T × T/3 T = 12 
2 T = 3 × 12 = 36 
T = 36/2 = 18 days i.e. No. of days taken by Tapas alone = 18 days.

22.

If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in 

   A.) 1 days
   B.) 1 ½ days
   C.) ¾ day
   D.) ½ day

Answer: Option 'A'

The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m 
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.

23.

Sam, Bob and Kim can do a job alone in 15 days, 10 days and 30 days respectively. Sam is helped by Bob and Kim every third day. In how many days will the job be completed? 

   A.) 9 days
   B.) 8 1/3 days
   C.) 8 days
   D.) 6 1/3 days

Answer: Option 'A'

The work done by the three persons in 3 days ( because Sam works only on every third day) 
= 3/15 + 1/10 + 1/30 = 6 + 3 + 1/30 = 10/30 
= 1/3 of the work 
Therefore, the job will be completed in 3 × 3 = 9 days.

24.

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 work?

   A.) 18 days
   B.) 24 days
   C.) 36 days
   D.) 30 days

Answer: Option 'A'

i.e. 2 ( A + B + C) ‘s 1 day’s work = 1/30 + 1/24 + 1/20 = 1/8 
their 1 day’s work = 1/8/2 = 1/16 
their 10 days work = 1/16 × 10 = 5/8 
the remaining work = 3/8 
A’s 1 day’s work = 1/16 – 1/24 = 1/48 
Therefore, the No. of days A alone will take to complete 3/8 of the work = 3/8/ 1/48
= 3/8 × 48 = 3 × 6 = 18 days.

25.

Three men, four women and six children can complete a work in 7 days . A woman does double the work a man does and a child does half the work a man does. How many women can complete this work in 7 days? 

   A.) 8
   B.) 7
   C.) 12
   D.) 14

Answer: Option 'B'

3 men = 3/2 women 
1 child = 1/2/2 = ¼ woman 
Then, 6 children = ¼ × 6 = 6/4 = 3/2 women 
Then, 3/2 women + 4 women + 3/2 women = 7 women
7 women does the work in 7 days. 
Therefore, the No. of women required to finish the work in 7days = 7.


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