A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started together but A left 2 days after the start and B left 3 days before the completion of the work. How long did the work last? MCQ with Answer and Explanation
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Question #1
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A can complete a work in 31 days and B in 31 days. If both work together, in how many days will the work be completed?
Correct Answer: Option A
Explanation:
Combined rate = 1/31 + 1/31. Time = 15.5 days.
Combined rate = 1/31 + 1/31. Time = 15.5 days.
This question belongs to:
Maths
Time and Work
Question #2
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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?
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.
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.
This question belongs to:
Maths
Time and Work
Question #3
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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?
Correct Answer: Option A
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.
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.
This question belongs to:
Maths
Time and Work
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