Time and Work MCQs with Answers and Detailed Solutions

Question #101

A is twice as efficient as B and can finish a job in 20 days less than B. In how many days can they complete the work together?

A. 12 days

B. 13(1/3) days

C. 15 days

D. 14(2/3) days

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Correct Answer: Option B

Explanation:
Efficiency ratio A : B = 2 : 1. Time ratio A : B = 1 : 2. Difference = 1 part = 20 days. So A takes 20 days and B takes 40 days. Total work = 40 units. Combined efficiency = 3. Time taken together = 40 / 3 = 13(1/3) days.

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Question #102

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If 10 men can complete a project in 12 days, how many more men are required to finish it in 8 days?

A. 6

B. 5

C. 4

D. 8

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Correct Answer: Option B

Explanation:
Using M1 * D1 = M2 * D2: 10 * 12 = M2 * 8 => 120 = 8 * M2 => M2 = 15 men. More men required = 15 - 10 = 5.

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Question #103

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A and B can do a piece of work in 15 days and 10 days respectively. They started the work together, but A left after 2 days. In how many days will B complete the remaining work?

A. 5 days

B. 6 days

C. 7 days

D. 6(2/3) days

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Correct Answer: Option D

Explanation:
Total work = LCM(15, 10) = 30 units. Efficiency of A = 2, B = 3. Combined efficiency = 5. In 2 days, work done = 2 * 5 = 10 units. Remaining work = 30 - 10 = 20 units. Time taken by B to complete remaining work = 20 / 3 = 6(2/3) days.

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Question #104

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A and B can complete a piece of work in 24 days and 30 days respectively. Working together, what fraction of the work can they complete in 4 days?

A. 1/5

B. 4/15

C. 3/10

D. 7/20

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Correct Answer: Option C

Explanation:
Total work = LCM(24, 30) = 120 units. Efficiency of A = 5, B = 4. Combined efficiency = 9 units/day. In 4 days, work completed = 4 * 9 = 36 units. Fraction of work completed = 36 / 120 = 3 / 10.

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Question #105

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A can complete a piece of work in 10 days, B in 15 days, and C in 20 days. A and C worked together for 2 days and then A was replaced by B. In how many days altogether was the work completed?

A. 9 days

B. 6 days

C. 8 days

D. 7 days

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Correct Answer: Option C

Explanation:
Total work = LCM(10, 15, 20) = 60 units. Efficiency of A = 6, B = 4, C = 3. A and C work for 2 days: work done = 2 * (6 + 3) = 18 units. Remaining work = 60 - 18 = 42 units. B and C complete remaining work together with efficiency = 4 + 3 = 7 units/day. Time taken for remaining work = 42 / 7 = 6 days. Total time = 2 + 6 = 8 days.

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Question #106

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If 8 men and 12 boys can finish a piece of work in 10 days, while 6 men and 8 boys can finish it in 14 days, find the time taken by 1 man alone to complete the work.

A. 120 days

B. 140 days

C. 160 days

D. 100 days

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Correct Answer: Option B

Explanation:
Total work = 10 * (8M + 12B) = 14 * (6M + 8B) => 80M + 120B = 84M + 112B => 4M = 8B => 1M = 2B. Total work = 10 * (8M + 6M) = 140M. Thus, 1 man alone will take 140 days.

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Question #107

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A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started the work together, but A left after 2 days and B left 3 days before the completion of the work. Find the total duration of the work.

A. 9 days

B. 6 days

C. 8 days

D. 7 days

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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. Let the work last for x days. A works for 2 days: work = 12 units. B works for (x - 3) days: work = 5(x - 3). C works for x days: work = 4x. Total work = 12 + 5x - 15 + 4x = 60 => 9x - 3 = 60 => 9x = 63 => x = 7 days.

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Question #108

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A can finish a work in 12 days and B can do it in 15 days. After A had worked for 3 days, B also joined him to finish the remaining work. In how many days was the remaining work completed?

A. 3 days

B. 6 days

C. 4 days

D. 5 days

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Correct Answer: Option D

Explanation:
Total work = LCM(12, 15) = 60 units. Efficiency of A = 5, B = 4. In 3 days, A completed 3 * 5 = 15 units. Remaining work = 60 - 15 = 45 units. Combined efficiency of A and B = 5 + 4 = 9 units/day. Time taken for remaining work = 45 / 9 = 5 days.

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Question #109

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A and B can complete a piece of work in 20 days and 30 days respectively. They work together for some days and then A leaves. If B completes the remaining work in 10 days, for how many days did they work together?

A. 6 days

B. 10 days

C. 8 days

D. 12 days

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Correct Answer: Option C

Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. B works alone for 10 days: work completed = 10 * 2 = 20 units. Remaining work = 60 - 20 = 40 units. This was done by A and B together. Combined efficiency = 3 + 2 = 5 units/day. Days worked together = 40 / 5 = 8 days.

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Question #110

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A, B and C can complete a piece of work in 10, 15 and 20 days respectively. They started together but A left after 2 days and B left 2 days before the completion of the work. Find the total number of days taken to complete the work.

A. 7 days

B. 9 days

C. 6 days

D. 8 days

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Correct Answer: Option D

Explanation:
Total work = LCM(10, 15, 20) = 60 units. Efficiency of A = 6, B = 4, C = 3. Let the total work last for x days. A worked for 2 days, so work done = 2 * 6 = 12 units. Remaining work = 60 - 12 = 48 units. B worked for (x - 2) days and C worked for x days. Therefore, 4(x - 2) + 3x = 48 => 4x - 8 + 3x = 48 => 7x = 56 => x = 8 days.

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Question #111

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If 12 men or 18 women can reap a field in 14 days, then the number of days that 8 men and 16 women will take to reap it is:

A. 10 days

B. 7 days

C. 9 days

D. 8 days

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Correct Answer: Option C

Explanation:
12 Men = 18 Women => 1 Man = 1.5 Women. 8 men + 16 women = 8 * 1.5 + 16 = 12 + 16 = 28 women. Since 18 women take 14 days, 28 women will take (18 * 14) / 28 = 252 / 28 = 9 days.

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Question #112

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A can do a piece of work in 24 days and B in 30 days. They work together for 6 days and then A leaves. How many days will B take to complete the remaining work?

A. 15 days

B. 18.5 days

C. 16.5 days

D. 14 days

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Correct Answer: Option C

Explanation:
Total work = LCM(24, 30) = 120 units. Efficiency of A = 5, B = 4. Combined efficiency = 9. In 6 days, work done = 6 * 9 = 54 units. Remaining work = 120 - 54 = 66 units. Time taken by B to complete the remaining work = 66 / 4 = 16.5 days.

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Question #113

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A can complete a project in 20 days and B in 30 days. If they work on alternate days starting with A, in how many days will the project be completed?

A. 26 days

B. 25 days

C. 24 days

D. 22 days

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Correct Answer: Option C

Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. In a 2-day cycle (A then B), work completed = 3 + 2 = 5 units. Number of cycles required = 60 / 5 = 12 cycles. Total time = 12 * 2 = 24 days.

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Question #114

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A is twice as fast as B and B is twice as fast as C. If they together can complete a work in 4 days, in how many days can C alone complete it?

A. 16 days

B. 24 days

C. 32 days

D. 28 days

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Correct Answer: Option D

Explanation:
Let efficiency of C = 1, then B = 2 and A = 4. Combined efficiency = 1 + 2 + 4 = 7 units/day. Total work = 4 * 7 = 28 units. Time taken by C alone = 28 / 1 = 28 days.

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Question #115

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A and B can do a piece of work in 10 days, B and C in 12 days, and C and A in 15 days. How long will C alone take to complete the work?

A. 60 days

B. 40 days

C. 24 days

D. 30 days

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Correct Answer: Option B

Explanation:
Total work = LCM(10, 12, 15) = 60 units. Efficiency of (A+B) = 6, (B+C) = 5, (C+A) = 4. Summing gives 2*(A+B+C) = 15 => Efficiency of (A+B+C) = 7.5. Efficiency of C = (A+B+C) - (A+B) = 7.5 - 6 = 1.5. Time taken by C alone = 60 / 1.5 = 40 days.

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Question #116

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A can finish a work in 15 days and B in 20 days. They work together for 6 days and then B leaves. In how many days will A finish the remaining work?

A. 5 days

B. 4.5 days

C. 6 days

D. 3.5 days

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Correct Answer: Option B

Explanation:
Total work = LCM(15, 20) = 60 units. Efficiency of A = 4, B = 3. Combined efficiency = 7. In 6 days, work done = 6 * 7 = 42 units. Remaining work = 60 - 42 = 18 units. Time taken by A to complete remaining work = 18 / 4 = 4.5 days.

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Question #117

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A and B together can do a piece of work in 9 days. If A does thrice the work of B in a given time, how many days will A alone take to complete the total work?

A. 12 days

B. 18 days

C. 15 days

D. 16 days

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Correct Answer: Option A

Explanation:
Ratio of efficiency of A : B = 3 : 1. Combined efficiency = 3 + 1 = 4. Total work = 9 * 4 = 36 units. Time taken by A alone = 36 / 3 = 12 days.

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Question #118

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A can complete a piece of work in 16 days and B in 12 days. Starting with A, they work on alternate days. In how many days will the total work be completed?

A. 12(2/3) days

B. 13(3/4) days

C. 14 days

D. 13(1/2) days

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Correct Answer: Option B

Explanation:
Total work = LCM(16, 12) = 48 units. Efficiency of A = 3, B = 4. In a 2-day cycle (A then B), work completed = 3 + 4 = 7 units. In 6 cycles (12 days), work completed = 7 * 6 = 42 units. Remaining work = 48 - 42 = 6 units. On Day 13, A works and completes 3 units. Remaining work = 3 units. On Day 14, B works with efficiency 4, so time taken = 3/4 day. Total time = 12 + 1 + 3/4 = 13(3/4) days.

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Question #119

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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 the work?

A. 50 days

B. 40 days

C. 45 days

D. 35 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 = 8 * (4*11W + 6W) = 8 * 50W = 400W. Time taken by 10 women = 400W / 10W = 40 days.

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Question #120

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A and B can do a work in 12 days, B and C in 15 days, and C and A in 20 days. How many days will A alone take to finish the work?

A. 30 days

B. 40 days

C. 20 days

D. 60 days

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Correct Answer: Option A

Explanation:
Total work = LCM(12, 15, 20) = 60 units. Efficiency of (A+B) = 5, (B+C) = 4, (C+A) = 3. Summing efficiencies gives 2*(A+B+C) = 12 => Efficiency of (A+B+C) = 6 units/day. Efficiency of A = (A+B+C) - (B+C) = 6 - 4 = 2 units/day. Time taken by A alone = 60 / 2 = 30 days.

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