Time and Work MCQs with Answers and Detailed Solutions

Question #21

A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work can they finish in a day?

A. 2/5

B. 1/9

C. 1/4

D. 1/6

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Correct Answer: Option D

Explanation:
Time taken by A = 18 days, so B takes 9 days. Efficiency of A = 1/18, B = 1/9. Together in one day = 1/18 + 1/9 = 3/18 = 1/6.

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Question #22

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A and B can do a piece of work in 45 and 40 days respectively. They began the work together, but A left after some days and B finished the remaining work in 23 days. After how many days did A leave?

A. 12 days

B. 6 days

C. 8 days

D. 9 days

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Correct Answer: Option D

Explanation:
Total work = LCM(45, 40) = 360 units. Efficiency of A = 8, B = 9. B worked alone for 23 days: work done = 23 * 9 = 207 units. Remaining work = 360 - 207 = 153 units. This was done by A and B together. Combined efficiency = 8 + 9 = 17. Number of days they worked together = 153 / 17 = 9 days. Thus, A left after 9 days.

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Question #23

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A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave. Then C alone finishes the remaining work in 10 days. In how many days can C alone finish the full work?

A. 24 days

B. 35 days

C. 25 days

D. 30 days

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Correct Answer: Option A

Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. Combined efficiency = 5 units/day. In 7 days, work done = 7 * 5 = 35 units. Remaining work = 60 - 35 = 25 units. C takes 10 days to do 25 units, so efficiency of C = 25 / 10 = 2.5 units/day. Time taken by C for full work = 60 / 2.5 = 24 days.

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Question #24

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If 10 men or 20 women can do a piece of work in 13 days, in how many days will 24 men and 17 women complete the same work?

A. 7 days

B. 5 days

C. 6 days

D. 4 days

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Correct Answer: Option D

Explanation:
10 Men = 20 Women => 1 Man = 2 Women. 24 men + 17 women = 24 * 2 + 17 = 48 + 17 = 65 women. Since 20 women do the work in 13 days, 65 women will do it in (20 * 13) / 65 = 260 / 65 = 4 days.

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Question #25

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A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?

A. 80

B. 83

C. 82

D. 81

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Correct Answer: Option D

Explanation:
Remaining days = 46 - 33 = 13 days. Remaining work = 1 - 4/7 = 3/7. Using (M1 * D1 * H1) / W1 = (M2 * D2 * H2) / W2: (117 * 33 * 8) / (4/7) = (M2 * 13 * 9) / (3/7) => (117 * 33 * 8) / 4 = (M2 * 13 * 9) / 3 => 117 * 33 * 2 = M2 * 13 * 3 => 117 * 33 * 2 = 39 * M2 => M2 = (117 * 33 * 2) / 39 = 3 * 33 * 2 = 198 men. Additional men = 198 - 117 = 81.

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Question #26

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A can do a piece of work in 14 days and B in 21 days. They begin together but 3 days before the completion of the work, A leaves. The total number of days taken to complete the work is:

A. 9(1/5) days

B. 8(3/5) days

C. 7(2/5) days

D. 10(1/5) days

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Correct Answer: Option D

Explanation:
Total work = LCM(14, 21) = 42 units. Efficiency of A = 3, B = 2. Let total days be x. A works for (x - 3) days and B works for x days. 3*(x - 3) + 2*x = 42 => 3x - 9 + 2x = 42 => 5x = 51 => x = 51/5 = 10(1/5) days.

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Question #27

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A and B can do a job in 12 days and 16 days respectively. Both work together for 3 days and then A leaves. How long will B take to complete the remaining work?

A. 8 days

B. 7 days

C. 9 days

D. 10 days

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Correct Answer: Option C

Explanation:
Total work = LCM(12, 16) = 48 units. Efficiency of A = 4, B = 3. Combined efficiency = 7 units/day. In 3 days, work completed = 7 * 3 = 21 units. Remaining work = 48 - 21 = 27 units. Time taken by B for remaining work = 27 / 3 = 9 days.

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Question #28

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A can build a wall in 20 days, while B can destroy it in 30 days. If they work on alternate days starting with A, in how many days will the wall be completely built?

A. 120 days

B. 115 days

C. 116 days

D. 113 days

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Correct Answer: Option B

Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = +3, B = -2. In 2 days (A then B), net work done = 3 - 2 = 1 unit. We need to reach 60 units. Since A can add 3 units on his turn, we find when work reaches 60 - 3 = 57 units. 57 units will be done in 57 * 2 = 114 days. On the 115th day, A works and completes 3 units, making the total work 57 + 3 = 60 units. So, the wall is built in 115 days.

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Question #29

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A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days will the work be completed?

A. 10(1/2) days

B. 10(1/4) days

C. 11 days

D. 10 days

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Correct Answer: Option B

Explanation:
Total work = LCM(9, 12) = 36 units. Efficiency of A = 4, B = 3. In 2 days (A + B), work done = 4 + 3 = 7 units. In 10 days (5 pairs of 2 days), work done = 7 * 5 = 35 units. Remaining work = 36 - 35 = 1 unit. On the 11th day, it is A's turn. Time taken by A to complete 1 unit = 1/4 day. Total time = 10 + 1/4 = 10(1/4) days.

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Question #30

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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 days

B. 40 days

C. 45 days

D. 50 days

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Correct Answer: Option B

Explanation:
Total work = 8 * (4M + 6W) = 10 * (3M + 7W) => 32M + 48W = 30M + 70W => 2M = 22W => 1M = 11W. Total work in terms of women = 8 * (4*11W + 6W) = 8 * 50W = 400 W-days. Time taken by 10 women = 400 / 10 = 40 days.

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Question #31

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A is 30% more efficient than B. How much time will they take together to complete a job which A alone can finish in 23 days?

A. 11 days

B. 14 days

C. 12 days

D. 13 days

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Correct Answer: Option D

Explanation:
Let efficiency of B = 10, then efficiency of A = 13. Total work = Efficiency of A * Time taken by A = 13 * 23 = 299 units. Combined efficiency of A and B = 13 + 10 = 23. Time taken together = 299 / 23 = 13 days.

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Question #32

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A tank can be filled by pipe A in 6 hours and emptied by pipe B in 8 hours. If both pipes are opened together, how much time will it take to fill the empty tank?

A. 18 hours

B. 24 hours

C. 12 hours

D. 14 hours

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Correct Answer: Option B

Explanation:
Total capacity = LCM(6, 8) = 24 units. Efficiency of A = +4, B = -3. Combined efficiency = 4 - 3 = 1 unit/hour. Time required = 24 / 1 = 24 hours.

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Question #33

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Two pipes A and B can fill a cistern in 12 minutes and 15 minutes respectively. There is also a waste pipe C. If all three pipes are opened together, the cistern is full in 20 minutes. How long will C take to empty the full cistern?

A. 8 minutes

B. 10 minutes

C. 12 minutes

D. 15 minutes

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Correct Answer: Option B

Explanation:
Total capacity = LCM(12, 15, 20) = 60 units. Efficiency of A = 5, B = 4. Combined efficiency of A+B+C = 3. Efficiency of C = 3 - (5 + 4) = -6. Thus, C empties 6 units/minute. Time taken by C to empty the full cistern = 60 / 6 = 10 minutes.

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Question #34

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Three pumps working 8 hours a day can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the same tank in 1 day?

A. 15 hours

B. 12 hours

C. 10 hours

D. 16 hours

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Correct Answer: Option B

Explanation:
Using P1 * D1 * H1 = P2 * D2 * H2: 3 * 2 * 8 = 4 * 1 * H2 => 48 = 4 * H2 => H2 = 12 hours.

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Question #35

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A and B can do a piece of work in 10 days and 15 days respectively. They work together for 2 days and then A is replaced by C. The work is finished in next 4 days. In how many days can C alone finish the work?

A. 10 days

B. 12 days

C. 8 days

D. 15 days

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Correct Answer: Option A

Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. In 2 days, A and B do 2 * (3 + 2) = 10 units. Remaining work = 30 - 10 = 20 units. This is completed by B and C in 4 days, so combined efficiency of B and C = 20 / 4 = 5 units/day. Since efficiency of B = 2, efficiency of C = 5 - 2 = 3 units/day. Time taken by C alone = 30 / 3 = 10 days.

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Question #36

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A team of 30 men is supposed to do a work in 38 days. After 25 days, 5 more men were employed and the work was finished one day earlier than the scheduled time. How many days would it have been delayed if 5 more men were not employed?

A. 2 days

B. 3 days

C. 4 days

D. 1 day

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Correct Answer: Option D

Explanation:
Scheduled time = 38 days. Work finished 1 day earlier, so it took 37 days. For the first 25 days, 30 men worked. For the remaining 37 - 25 = 12 days, 35 men worked. Remaining work = 35 * 12 = 420 man-days. If 5 extra men were not joined, 30 men would take 420 / 30 = 14 days to complete this remaining work. Total days taken without extra men = 25 + 14 = 39 days. Delay = 39 - 38 = 1 day.

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Question #37

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A and B can complete a work together in 15 days. They work together for 3 days, then A leaves. If B alone completes the remaining work in 16 days, in how many days can A alone complete the whole work?

A. 75 days

B. 60 days

C. 45 days

D. 30 days

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Correct Answer: Option B

Explanation:
Let the total work be 60 units. Combined efficiency of A and B = 60 / 15 = 4 units/day. In 3 days, they complete 3 * 4 = 12 units. Remaining work = 60 - 12 = 48 units. B completes 48 units in 16 days, so B's efficiency = 48 / 16 = 3 units/day. A's efficiency = 4 - 3 = 1 unit/day. Time taken by A alone = 60 / 1 = 60 days.

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Question #38

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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. 25 days

B. 35 days

C. 30 days

D. 20 days

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Correct Answer: Option A

Explanation:
Total work = LCM(10, 50) = 50 units. Efficiency of (A + B) = 5, efficiency of C = 1. Total efficiency of (A + B + C) = 5 + 1 = 6. Given A = B + C. So, (B + C) + B + C = 6 => 2(B + C) = 6 => B + C = 3. Since C = 1, B = 2. Time taken by B alone = 50 / 2 = 25 days.

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Question #39

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

A. 100

B. 55

C. 110

D. 120

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Correct Answer: Option C

Explanation:
Let the original number of workers be x. Using M1 * D1 = M2 * D2: x * 100 = (x - 10) * 110 => 100x = 110x - 1100 => 10x = 1100 => x = 110.

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Question #40

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A, B and C can do a 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. 16 days

B. 12 days

C. 15 days

D. 18 days

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Correct Answer: Option C

Explanation:
Total work = LCM(20, 30, 60) = 60 units. Efficiency of A = 3, B = 2, C = 1. Day 1: A works (3 units). Day 2: A works (3 units). Day 3: A, B, and C work together (3 + 2 + 1 = 6 units). Total work in 3 days = 3 + 3 + 6 = 12 units. To complete 60 units, number of 3-day cycles needed = 60 / 12 = 5 cycles. Total days = 5 * 3 = 15 days.

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