A and B can do a piece of work in 45 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? MCQ with Answer and Explanation
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Question #1
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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 D
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 #2
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A can complete a work in 16 days and B in 20 days. If both work together, in how many days will the work be completed?
Correct Answer: Option A
Explanation:
Combined rate = 1/16 + 1/20. Time = 8.89 days.
Combined rate = 1/16 + 1/20. Time = 8.89 days.
This question belongs to:
Maths
Time and Work
Question #3
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A and B can complete a work in 12 days and 16 days respectively. Both work together for 3 days and then A leaves. How long will B take to complete the remaining work?
Correct Answer: Option C
Explanation:
Total work = LCM(12, 16) = 48 units. Efficiency of A = 4, B = 3. Combined efficiency = 7 units/day. In 3 days, work completed = 3 * 7 = 21 units. Remaining work = 48 - 21 = 27 units. Time taken by B to complete remaining work = 27 / 3 = 9 days.
Total work = LCM(12, 16) = 48 units. Efficiency of A = 4, B = 3. Combined efficiency = 7 units/day. In 3 days, work completed = 3 * 7 = 21 units. Remaining work = 48 - 21 = 27 units. Time taken by B to complete remaining work = 27 / 3 = 9 days.
This question belongs to:
Maths
Time and Work
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