Time and Work MCQs with Answers and Detailed Solutions

Question #81

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A is 20% less efficient than B. If A can complete a work in 15 days, in how many days will B complete it?

A. 12 days

B. 9 days

C. 11 days

D. 10 days

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Correct Answer: Option A

Explanation:
Let efficiency of B = 5, then efficiency of A = 4. Total work = Efficiency of A * Time of A = 4 * 15 = 60 units. Time taken by B = 60 / 5 = 12 days.

This question belongs to: Maths Time and Work

Question #82

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A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days can A alone finish the remaining work?

A. 6 days

B. 5 days

C. 5(1/2) days

D. 8 days

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Correct Answer: Option A

Explanation:
Total work = LCM(18, 15) = 90 units. Efficiency of A = 5, B = 6. B works for 10 days: work done = 10 * 6 = 60 units. Remaining work = 90 - 60 = 30 units. Time taken by A to finish the remaining work = 30 / 5 = 6 days.

This question belongs to: Maths Time and Work

Question #83

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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. In how many days can A alone complete the work?

A. 24 days

B. 20 days

C. 30 days

D. 40 days

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Correct Answer: Option C

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

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Question #84

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

A. 8(3/5) days

B. 9(1/5) days

C. 11(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) + 2x = 42 => 3x - 9 + 2x = 42 => 5x = 51 => x = 51/5 = 10(1/5) days.

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Question #85

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10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work be completed?

A. 7 days

B. 6(1/3) days

C. 8 days

D. 6(2/3) days

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Correct Answer: Option D

Explanation:
1-day work of 10 men = 1/15. 1-day work of 15 women = 1/12. Combined 1-day work = 1/15 + 1/12 = (4 + 5) / 60 = 9 / 60 = 3 / 20. Total days required = 20 / 3 = 6(2/3) days.

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Question #86

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A is twice as efficient as B and B is twice as efficient as C. If A and B together can complete a work in 4 days, then C alone can complete it in:

A. 32 days

B. 24 days

C. 12 days

D. 16 days

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Correct Answer: Option B

Explanation:
Let efficiency of C = 1. Then efficiency of B = 2 and efficiency of A = 4. Combined efficiency of A and B = 4 + 2 = 6. Total work = 4 * 6 = 24 units. Time taken by C alone = 24 / 1 = 24 days.

This question belongs to: Maths Time and Work

Question #87

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A can do a piece of work in 10 days and B can do the same work in 15 days. If they work together on alternate days starting with A, in how many days will the work be completed?

A. 11 days

B. 12 days

C. 10 days

D. 13 days

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Correct Answer: Option B

Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. In a 2-day cycle (A then B), work done = 3 + 2 = 5 units. Number of cycles required to complete 30 units = 30 / 5 = 6 cycles. Total days = 6 * 2 = 12 days.

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Question #88

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A and B together can complete a piece of work in 8 days. If A alone can complete the same work in 12 days, in how many days can B alone complete it?

A. 18 days

B. 24 days

C. 20 days

D. 16 days

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Correct Answer: Option B

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

This question belongs to: Maths Time and Work

Question #89

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A can finish a 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. 25 days

C. 30 days

D. 20 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 completed = 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 alone for full work = 60 / 2.5 = 24 days.

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Question #90

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A, B and C can complete a piece of work in 12, 15 and 20 days respectively. If they work together, what is the ratio of their wages?

A. 5 : 4 : 3

B. 5 : 3 : 4

C. 4 : 5 : 6

D. 3 : 4 : 5

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Correct Answer: Option A

Explanation:
Wages are distributed in the ratio of their efficiencies. Ratio of time taken = 12 : 15 : 20. Ratio of efficiencies = 1/12 : 1/15 : 1/20. Multiplying by LCM (60), we get 5 : 4 : 3.

This question belongs to: Maths Time and Work

Question #91

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A and B can do a piece of work in 45 days 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. 9 days

B. 8 days

C. 6 days

D. 12 days

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Correct Answer: Option A

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

This question belongs to: Maths Time and Work

Question #92

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If 20 men can build a wall 56 meters long in 6 days, what length of a similar wall can be built by 35 men in 3 days?

A. 49 meters

B. 52 meters

C. 56 meters

D. 42 meters

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Correct Answer: Option A

Explanation:
Using (M1 * D1) / W1 = (M2 * D2) / W2: (20 * 6) / 56 = (35 * 3) / W2 => 120 / 56 = 105 / W2 => W2 = (105 * 56) / 120 = (7 * 56) / 8 = 7 * 7 = 49 meters.

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Question #93

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A can do a piece of work in 10 days, B in 15 days. They work together for 2 days and then A leaves. In how many days will B complete the remaining work?

A. 12 days

B. 11 days

C. 10 days

D. 8 days

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Correct Answer: Option C

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

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Question #94

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

A. 24 days

B. 23 days

C. 25 days

D. 26 days

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Correct Answer: Option A

Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. In 2 days (B then A), work completed = 2 + 3 = 5 units. Time taken to complete 60 units = (60 / 5) * 2 = 24 days.

This question belongs to: Maths Time and Work

Question #95

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A, B and C together can earn Rs. 300 per day, while A and C together can earn Rs. 188 and B and C together can earn Rs. 152. Find the daily earning of C.

A. Rs. 50

B. Rs. 40

C. Rs. 60

D. Rs. 112

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Correct Answer: Option B

Explanation:
Given: A + B + C = 300, A + C = 188, B + C = 152. Substitute A + C in the first equation: 188 + B = 300 => B = 112. Now substitute B in B + C = 152: 112 + C = 152 => C = 40. Thus, C's earning is Rs. 40.

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Question #96

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A is twice as fast as B. If B can complete a work in 12 days, in how many days can A and B together complete the work?

A. 8 days

B. 4 days

C. 6 days

D. 3 days

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Correct Answer: Option B

Explanation:
B takes 12 days, so A takes 6 days. Total work = 12 units. Efficiency of A = 2, B = 1. Combined efficiency = 3 units/day. Time taken together = 12 / 3 = 4 days.

This question belongs to: Maths Time and Work

Question #97

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A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can B alone complete the work?

A. 20 days

B. 60 days

C. 30 days

D. 40 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. Efficiency of B = (A+B+C) - (C+A) = 6 - 3 = 3. Time taken by B alone = 60 / 3 = 20 days.

This question belongs to: Maths Time and Work

Question #98

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A can do a work in 4 days, B in 5 days and C in 10 days. Find the time taken by A, B and C together to do the work.

A. 1(7/11) days

B. 2(1/11) days

C. 1(9/11) days

D. 2 days

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Correct Answer: Option C

Explanation:
Total work = LCM(4, 5, 10) = 20 units. Efficiency of A = 5, B = 4, C = 2. Combined efficiency = 5 + 4 + 2 = 11 units/day. Time taken together = 20 / 11 = 1(9/11) days.

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Question #99

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A factory produces 6000 toys in 12 days working 8 hours a day. How many toys can it produce in 15 days working 6 hours a day?

A. 6000 toys

B. 6250 toys

C. 5800 toys

D. 5625 toys

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Correct Answer: Option D

Explanation:
Using (D1 * H1) / W1 = (D2 * H2) / W2: (12 * 8) / 6000 = (15 * 6) / W2 => 96 / 6000 = 90 / W2 => W2 = (90 * 6000) / 96 = 540000 / 96 = 5625 toys.

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Question #100

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A can build a wall in 30 days, while B can destroy it in 40 days. If they work on alternate days starting with A, in how many days will the wall be built?

A. 235 days

B. 233 days

C. 237 days

D. 240 days

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Correct Answer: Option B

Explanation:
Total work = LCM(30, 40) = 120 units. Efficiency of A = +4, B = -3. In 2 days, net work = 4 - 3 = 1 unit. We look for when the work reaches 120 - 4 = 116 units. 116 units are done in 116 * 2 = 232 days. On the 233rd day, A works and completes 4 units, making total work 116 + 4 = 120 units. Thus, the wall is completed in 233 days.

This question belongs to: Maths Time and Work

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