Time and Work MCQs with Answers and Detailed Solutions

Question #141

A can build a wall in 15 days, and B can destroy it in 20 days. If they work on alternate days starting with A, in how many days will the wall be built?

A. 115 days

B. 120 days

C. 117 days

D. 113 days

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Correct Answer: Option D

Explanation:
Total work = LCM(15, 20) = 60 units. Efficiency of A = +4, B = -3. In 2 days (A then B), net work done = 4 - 3 = 1 unit. We need to reach 60 - 4 = 56 units first. 56 units will be done in 56 * 2 = 112 days. On the 113th day, A works and completes 4 units, making the total work 56 + 4 = 60 units. So, the wall is completed in 113 days.

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Question #142

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A and B can complete a work in 10 days and 15 days respectively. They started together, but A left after some days and B finished the remaining work in 5 days. After how many days did A leave?

A. 2 days

B. 3 days

C. 4 days

D. 5 days

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Correct Answer: Option C

Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. B worked alone for 5 days: work done = 5 * 2 = 10 units. Remaining work = 30 - 10 = 20 units. This was completed by A and B together. Combined efficiency = 3 + 2 = 5 units/day. Time they worked together = 20 / 5 = 4 days. Thus, A left after 4 days.

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Question #143

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A is twice as efficient as B, and C is thrice as efficient as B. If they working together can finish a work in 5 days, in how many days can A alone finish it?

A. 18 days

B. 12 days

C. 10 days

D. 15 days

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Correct Answer: Option D

Explanation:
Let efficiency of B = 1. Then efficiency of A = 2, and efficiency of C = 3. Combined efficiency = 1 + 2 + 3 = 6. Total work = 5 * 6 = 30 units. Time taken by A alone = 30 / 2 = 15 days.

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Question #144

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X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 14 days, Y alone can finish that work in:

A. 30 days

B. 18 days

C. 24 days

D. 20 days

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Correct Answer: Option C

Explanation:
Let total work be 24 units. Efficiency of X = 1 unit/day. X worked for all 14 days, so work done by X = 14 * 1 = 14 units. Remaining work = 24 - 14 = 10 units. This 10 units of work was done by Y. Y worked for 14 - 4 = 10 days. So Y's efficiency = 10 / 10 = 1 unit/day. Time taken by Y alone = 24 / 1 = 24 days.

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Question #145

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A can finish a work in 10 days and B in 15 days. B starts the work and is joined by A after 5 days. What is the total number of days taken to complete the work?

A. 7 days

B. 9 days

C. 8 days

D. 6 days

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Correct Answer: Option B

Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. B works alone for 5 days: work completed = 5 * 2 = 10 units. Remaining work = 30 - 10 = 20 units. Now A and B work together with efficiency = 3 + 2 = 5 units/day. Time taken for remaining work = 20 / 5 = 4 days. Total time = 5 + 4 = 9 days.

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Question #146

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12 men can complete a piece of work in 12 days. If 6 men leave after 6 days, how many more days will it take to complete the remaining work?

A. 8 days

B. 12 days

C. 6 days

D. 10 days

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Correct Answer: Option B

Explanation:
Total work = 12 * 12 = 144 man-days. In 6 days, 12 men complete = 12 * 6 = 72 man-days. Remaining work = 144 - 72 = 72 man-days. Remaining men = 12 - 6 = 6 men. Time taken by 6 men to complete remaining work = 72 / 6 = 12 days.

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Question #147

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A can do a piece of work in 24 days, B in 32 days, and C in 64 days. They start together but A leaves after 6 days and B leaves 6 days before the completion of the work. Find the total number of days taken to complete the work.

A. 18 days

B. 20 days

C. 16 days

D. 24 days

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Correct Answer: Option B

Explanation:
Total work = LCM(24, 32, 64) = 192 units. Efficiency of A = 8, B = 6, C = 3. Let total days be x. A works for 6 days. B works for (x - 6) days. C works for x days. Total work = 6*8 + (x - 6)*6 + x*3 = 192 => 48 + 6x - 36 + 3x = 192 => 9x + 12 = 192 => 9x = 180 => x = 20 days.

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Question #148

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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. 4500 as wages. Find the share of C.

A. Rs. 1200

B. Rs. 1500

C. Rs. 1000

D. Rs. 1800

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Correct Answer: Option A

Explanation:
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Ratio of wages = 6 : 5 : 4. Total ratio parts = 15. Share of C = (4 / 15) * 4500 = 4 * 300 = Rs. 1200.

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Question #149

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A can complete a work in 11 days and B can complete the same work in 16 days. If they work together, in how many days will the work be completed?

A. 8.52

B. 6.52

C. 10.52

D. 12.52

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Correct Answer: Option B

Explanation:
Combined rate = 1/11 + 1/16. Time = 1 ÷ combined rate = 6.52 days.

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Question #150

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A can complete a work in 12 days and B can complete the same work in 17 days. If they work together, in how many days will the work be completed?

A. 11.03

B. 7.03

C. 13.03

D. 9.03

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Correct Answer: Option B

Explanation:
Combined rate = 1/12 + 1/17. Time = 1 ÷ combined rate = 7.03 days.

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Question #151

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A can complete a work in 13 days and B can complete the same work in 18 days. If they work together, in how many days will the work be completed?

A. 13.55

B. 11.55

C. 9.55

D. 7.55

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Correct Answer: Option D

Explanation:
Combined rate = 1/13 + 1/18. Time = 1 ÷ combined rate = 7.55 days.

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Question #152

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A can complete a work in 14 days and B can complete the same work in 19 days. If they work together, in how many days will the work be completed?

A. 12.06

B. 14.06

C. 8.06

D. 10.06

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Correct Answer: Option C

Explanation:
Combined rate = 1/14 + 1/19. Time = 1 ÷ combined rate = 8.06 days.

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Question #153

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A can complete a work in 15 days and B can complete the same work in 20 days. If they work together, in how many days will the work be completed?

A. 8.57

B. 12.57

C. 10.57

D. 14.57

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Correct Answer: Option A

Explanation:
Combined rate = 1/15 + 1/20. Time = 1 ÷ combined rate = 8.57 days.

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Question #154

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A can complete a work in 16 days and B can complete the same work in 21 days. If they work together, in how many days will the work be completed?

A. 13.08

B. 9.08

C. 11.08

D. 15.08

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Correct Answer: Option B

Explanation:
Combined rate = 1/16 + 1/21. Time = 1 ÷ combined rate = 9.08 days.

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Question #155

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A can complete a work in 17 days and B can complete the same work in 22 days. If they work together, in how many days will the work be completed?

A. 13.59

B. 9.59

C. 15.59

D. 11.59

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Correct Answer: Option B

Explanation:
Combined rate = 1/17 + 1/22. Time = 1 ÷ combined rate = 9.59 days.

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Question #156

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A can complete a work in 18 days and B can complete the same work in 23 days. If they work together, in how many days will the work be completed?

A. 12.1

B. 10.1

C. 14.1

D. 16.1

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Correct Answer: Option B

Explanation:
Combined rate = 1/18 + 1/23. Time = 1 ÷ combined rate = 10.1 days.

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Question #157

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A can complete a work in 19 days and B can complete the same work in 24 days. If they work together, in how many days will the work be completed?

A. 16.6

B. 14.6

C. 12.6

D. 10.6

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Correct Answer: Option D

Explanation:
Combined rate = 1/19 + 1/24. Time = 1 ÷ combined rate = 10.6 days.

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Question #158

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A can complete a work in 20 days and B can complete the same work in 25 days. If they work together, in how many days will the work be completed?

A. 11.11

B. 15.11

C. 17.11

D. 13.11

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Correct Answer: Option A

Explanation:
Combined rate = 1/20 + 1/25. Time = 1 ÷ combined rate = 11.11 days.

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Question #159

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A can complete a work in 21 days and B can complete the same work in 26 days. If they work together, in how many days will the work be completed?

A. 17.62

B. 15.62

C. 13.62

D. 11.62

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Correct Answer: Option D

Explanation:
Combined rate = 1/21 + 1/26. Time = 1 ÷ combined rate = 11.62 days.

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Question #160

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A can complete a work in 22 days and B can complete the same work in 27 days. If they work together, in how many days will the work be completed?

A. 18.12

B. 16.12

C. 14.12

D. 12.12

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Correct Answer: Option D

Explanation:
Combined rate = 1/22 + 1/27. Time = 1 ÷ combined rate = 12.12 days.

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