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? MCQ with Answer and Explanation
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Question #1
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A can build a wall in 20 days, while B can destroy it in 30 days. If they work on alternate days starting with A, in how many days will the wall be completely built?
Correct Answer: Option A
Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = +3, B = -2. In 2 days (A then B), net work done = 3 - 2 = 1 unit. We need to reach 60 units. Since A can add 3 units on his turn, we find when work reaches 60 - 3 = 57 units. 57 units will be done in 57 * 2 = 114 days. On the 115th day, A works and completes 3 units, making the total work 57 + 3 = 60 units. So, the wall is built in 115 days.
Total work = LCM(20, 30) = 60 units. Efficiency of A = +3, B = -2. In 2 days (A then B), net work done = 3 - 2 = 1 unit. We need to reach 60 units. Since A can add 3 units on his turn, we find when work reaches 60 - 3 = 57 units. 57 units will be done in 57 * 2 = 114 days. On the 115th day, A works and completes 3 units, making the total work 57 + 3 = 60 units. So, the wall is built in 115 days.
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Maths
Time and Work
Question #2
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A is 50% more efficient than B. C does half of the work done by A and B together in the same time. If C alone can do the work in 40 days, then A, B and C together can do the work in:
Correct Answer: Option B
Explanation:
Let efficiency of B = 2, then efficiency of A = 3. Combined efficiency of A and B = 5. Efficiency of C = 5 / 2 = 2.5. Total work = Efficiency of C * Time taken by C = 2.5 * 40 = 100 units. Combined efficiency of A, B and C = 3 + 2 + 2.5 = 7.5 units/day. Time taken together = 100 / 7.5 = 1000 / 75 = 40 / 3 = 13(1/3) days.
Let efficiency of B = 2, then efficiency of A = 3. Combined efficiency of A and B = 5. Efficiency of C = 5 / 2 = 2.5. Total work = Efficiency of C * Time taken by C = 2.5 * 40 = 100 units. Combined efficiency of A, B and C = 3 + 2 + 2.5 = 7.5 units/day. Time taken together = 100 / 7.5 = 1000 / 75 = 40 / 3 = 13(1/3) days.
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Time and Work
Question #3
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A can do a piece of work in 15 days and B in 20 days. They began the work together but A left after 4 days. In how many days will B complete the remaining work?
Correct Answer: Option B
Explanation:
Total work = LCM(15, 20) = 60 units. Efficiency of A = 4, B = 3. Combined efficiency = 7. In 4 days, work completed = 4 * 7 = 28 units. Remaining work = 60 - 28 = 32 units. Time taken by B to complete remaining work = 32 / 3 = 10(2/3) days.
Total work = LCM(15, 20) = 60 units. Efficiency of A = 4, B = 3. Combined efficiency = 7. In 4 days, work completed = 4 * 7 = 28 units. Remaining work = 60 - 28 = 32 units. Time taken by B to complete remaining work = 32 / 3 = 10(2/3) days.
This question belongs to:
Maths
Time and Work
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