Time and Work MCQs with Answers and Detailed Solutions

Question #41

Two workers A and B are engaged to do a piece of work. Working together they would take 8 hours less than the time taken by A alone, and 4.5 hours less than the time taken by B alone. Find the time they take to complete the work together.

A. 8 hours

B. 6 hours

C. 7 hours

D. 5 hours

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Correct Answer: Option B

Explanation:
Let the time taken together be t hours. Then A takes (t + 8) hours and B takes (t + 4.5) hours. Using the direct formula for such problems: t = sqrt(a * b), where a and b are the extra times. t = sqrt(8 * 4.5) = sqrt(36) = 6 hours.

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Question #42

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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. 6 days

B. 5 days

C. 7 days

D. 4 days

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Correct Answer: Option D

Explanation:
Total work = 10 * (6M + 8B) = 2 * (26M + 48B) => 60M + 80B = 52M + 96B => 8M = 16B => 1M = 2B. Total work in terms of boys = 10 * (6*2B + 8B) = 10 * 20B = 200 boy-days. Efficiency of 15 men and 20 boys = 15*2B + 20B = 50B. Time taken = 200 / 50 = 4 days.

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Question #43

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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. 10.5 days

D. 10 days

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Correct Answer: Option D

Explanation:
Total work = LCM(24, 9, 12) = 72 units. Efficiency of A = 3, B = 8, C = 6. B and C work for 3 days: work done = 3 * (8 + 6) = 3 * 14 = 42 units. Remaining work = 72 - 42 = 30 units. Time taken by A to complete remaining work = 30 / 3 = 10 days.

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Question #44

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A group of men decided to do a work in 10 days, but 5 of them became absent. If the rest of the group did the work in 12 days, find the original number of men.

A. 30

B. 40

C. 35

D. 25

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Correct Answer: Option A

Explanation:
Let the original number of men be x. Using M1 * D1 = M2 * D2: x * 10 = (x - 5) * 12 => 10x = 12x - 60 => 2x = 60 => x = 30.

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Question #45

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A is thrice as efficient as B. Working together, they can complete a piece of work in 18 days. In how many days can A alone complete the work?

A. 54 days

B. 24 days

C. 72 days

D. 36 days

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Correct Answer: Option B

Explanation:
Let B's efficiency = 1, then A's efficiency = 3. Combined efficiency = 3 + 1 = 4. Total work = 18 * 4 = 72 units. Time taken by A alone = 72 / 3 = 24 days.

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Question #46

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A can do a piece of work in 40 days. He works at it for 8 days and then B finishes it in 16 days. How long will A and B together take to complete the work?

A. 13(1/3) days

B. 20 days

C. 15 days

D. 25 days

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Correct Answer: Option A

Explanation:
Let total work be 40 units. Efficiency of A = 1 unit/day. In 8 days, A completes 8 units. Remaining work = 40 - 8 = 32 units. B finishes 32 units in 16 days, so B's efficiency = 32 / 16 = 2 units/day. Combined efficiency of A and B = 1 + 2 = 3 units/day. Time taken together = 40 / 3 = 13(1/3) days.

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Question #47

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A and B together can complete a piece of work in 12 days. They worked together for 4 days and then A left. B finished the remaining work alone in 14 more days. In how many days can A alone complete the work?

A. 35 days

B. 42 days

C. 28 days

D. 21 days

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Correct Answer: Option C

Explanation:
Let combined efficiency of A and B be 1 unit/day, so total work = 12 units. In 4 days, they complete 4 units. Remaining work = 12 - 4 = 8 units. B completes 8 units in 14 days, so B's efficiency = 8 / 14 = 4/7 units/day. Efficiency of A = 1 - 4/7 = 3/7 units/day. Time taken by A alone = 12 / (3/7) = (12 * 7) / 3 = 28 days.

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Question #48

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A is 50% more efficient than B. C does half of the work done by A and B together in the same time. If C alone can do the work in 40 days, then A, B and C together can do the work in:

A. 20 days

B. 15 days

C. 13(1/3) days

D. 30 days

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Correct Answer: Option C

Explanation:
Let efficiency of B = 2, then efficiency of A = 3. Combined efficiency of A and B = 5. Efficiency of C = 5 / 2 = 2.5. Total work = Efficiency of C * Time taken by C = 2.5 * 40 = 100 units. Combined efficiency of A, B and C = 3 + 2 + 2.5 = 7.5 units/day. Time taken together = 100 / 7.5 = 1000 / 75 = 40 / 3 = 13(1/3) days.

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Question #49

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10 men can complete a work in 7 days. But 10 women can complete the same work in 14 days. If 5 men and 10 women work together, in how many days will the work be completed?

A. 6 days

B. 8 days

C. 7 days

D. 5 days

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Correct Answer: Option C

Explanation:
Efficiency of 10 men = 1/7, so 1 man = 1/70. Efficiency of 10 women = 1/14. Efficiency of 5 men and 10 women = 5*(1/70) + 1/14 = 1/14 + 1/14 = 2/14 = 1/7. Thus, they will complete the work in 7 days.

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Question #50

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A and B can complete a piece of work in 18 days and 24 days respectively. They worked together for 6 days and then A left. In how many days will B complete the remaining work?

A. 14 days

B. 8 days

C. 10 days

D. 12 days

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Correct Answer: Option C

Explanation:
Total work = LCM(18, 24) = 72 units. Efficiency of A = 4, B = 3. Combined efficiency = 7. In 6 days, work done = 6 * 7 = 42 units. Remaining work = 72 - 42 = 30 units. Time taken by B to finish remaining work = 30 / 3 = 10 days.

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Question #51

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A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days can A and B together complete the work?

A. 35 days

B. 24 days

C. 30 days

D. 25 days

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Correct Answer: Option C

Explanation:
Let total work be 80 units. Efficiency of A = 1 unit/day. In 10 days, A completes 10 units. Remaining work = 80 - 10 = 70 units. B finishes 70 units in 42 days, so B's efficiency = 70 / 42 = 5/3 units/day. Combined efficiency of A and B = 1 + 5/3 = 8/3 units/day. Time taken together = 80 / (8/3) = (80 * 3) / 8 = 30 days.

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Question #52

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A can do a piece of work in 10 days, B in 12 days and C in 15 days. They carry out the work together and get a total of Rs. 6000 as wages. Find the share of A.

A. Rs. 2000

B. Rs. 2500

C. Rs. 1800

D. Rs. 2400

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Correct Answer: Option D

Explanation:
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Ratio of wages is equal to ratio of efficiencies = 6 : 5 : 4. Total ratio parts = 6 + 5 + 4 = 15. Share of A = (6 / 15) * 6000 = 6 * 400 = Rs. 2400.

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Question #53

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A, B and C can do a piece of work in 20, 30 and 60 days respectively. If A works everyday and is assisted by B and C together on every third day, then in how many days will the work be completed?

A. 20 days

B. 15 days

C. 18 days

D. 12 days

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Correct Answer: Option B

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+C work = 3 + 2 + 1 = 6 units. Work done in 3 days = 3 + 3 + 6 = 12 units. Number of 3-day cycles to complete 60 units = 60 / 12 = 5 cycles. Total days = 5 * 3 = 15 days.

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Question #54

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A and B can complete a piece of work in 12 and 18 days respectively. They begin the work together, but A leaves 4 days before the completion of the work. For how many days did A and B work together?

A. 5.6 days

B. 4.4 days

C. 5 days

D. 6 days

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Correct Answer: Option A

Explanation:
Total work = LCM(12, 18) = 36 units. Efficiency of A = 3, B = 2. Let total days be x. B works for x days, A works for (x - 4) days. 3(x - 4) + 2x = 36 => 3x - 12 + 2x = 36 => 5x = 48 => x = 9.6 days. A and B worked together for x - 4 = 9.6 - 4 = 5.6 days.

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Question #55

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If 12 men and 16 boys can do a piece of work in 5 days; while 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is:

A. 3 : 2

B. 5 : 4

C. 3 : 1

D. 2 : 1

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Correct Answer: Option D

Explanation:
Total work = 5 * (12M + 16B) = 4 * (13M + 24B) => 60M + 80B = 52M + 96B => 8M = 16B => M/B = 16/8 = 2/1. Thus, the ratio is 2 : 1.

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Question #56

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A can do a piece of work in 25 days and B can finish it in 20 days. They work together for 5 days and then A leaves. In how many days will B finish the remaining work?

A. 9 days

B. 10 days

C. 12 days

D. 11 days

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Correct Answer: Option D

Explanation:
Total work = LCM(25, 20) = 100 units. Efficiency of A = 4, B = 5. Combined efficiency = 9 units/day. In 5 days, work done = 5 * 9 = 45 units. Remaining work = 100 - 45 = 55 units. Time taken by B to complete remaining work = 55 / 5 = 11 days.

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Question #57

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

A. 13(1/3) days

B. 16 days

C. 14 days

D. 15 days

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Correct Answer: Option A

Explanation:
Let total work be 40 units. Efficiency of X = 1 unit/day. In 8 days, X completes 8 units. Remaining work = 40 - 8 = 32 units. Y finishes 32 units in 16 days, so Y's efficiency = 32 / 16 = 2 units/day. Combined efficiency of X and Y = 1 + 2 = 3 units/day. Time taken together = 40 / 3 = 13(1/3) days.

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Question #58

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A and B can do a work in 8 days, B and C in 12 days and A, B, C together in 6 days. In how many days can A and C together complete the work?

A. 10 days

B. 6 days

C. 4 days

D. 8 days

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Correct Answer: Option D

Explanation:
Total work = LCM(8, 12, 6) = 24 units. Efficiency of (A+B) = 3, (B+C) = 2, (A+B+C) = 4. Efficiency of C = (A+B+C) - (A+B) = 4 - 3 = 1. Efficiency of A = (A+B+C) - (B+C) = 4 - 2 = 2. Combined efficiency of A and C = 2 + 1 = 3. Time taken by A and C together = 24 / 3 = 8 days.

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Question #59

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A can finish a work in 15 days and B in 25 days. They start together but B leaves 5 days before the completion of the work. Find the total number of days taken to complete the work.

A. 11.25 days

B. 10 days

C. 13.25 days

D. 12.5 days

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Correct Answer: Option A

Explanation:
Total work = LCM(15, 25) = 75 units. Efficiency of A = 5, B = 3. Let total days be x. A works for x days, B works for (x - 5) days. 5x + 3(x - 5) = 75 => 8x - 15 = 75 => 8x = 90 => x = 90/8 = 11.25 days.

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Question #60

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If 3 men or 4 women can plow a field in 43 days, how long will 7 men and 5 women take to plow it?

A. 15 days

B. 8 days

C. 10 days

D. 12 days

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Correct Answer: Option D

Explanation:
3 Men = 4 Women => 1 Man = 4/3 Women. 7 men + 5 women = 7 * (4/3) + 5 = 28/3 + 5 = 43/3 women. Since 4 women take 43 days, 43/3 women will take (4 * 43) / (43/3) = 4 * 3 = 12 days.

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