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? MCQ with Answer and Explanation
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Question #1
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A is twice as fast as B and B is thrice as fast as C. If C alone can complete the work in 24 days, in how many days can they together finish the work?
Correct Answer: Option A
Explanation:
Let efficiency of C = 1. Then efficiency of B = 3 * 1 = 3. Efficiency of A = 2 * 3 = 6. Total work = Efficiency of C * Time of C = 1 * 24 = 24 units. Combined efficiency of A, B and C = 6 + 3 + 1 = 10. Time taken together = 24 / 10 = 2.4 days.
Let efficiency of C = 1. Then efficiency of B = 3 * 1 = 3. Efficiency of A = 2 * 3 = 6. Total work = Efficiency of C * Time of C = 1 * 24 = 24 units. Combined efficiency of A, B and C = 6 + 3 + 1 = 10. Time taken together = 24 / 10 = 2.4 days.
This question belongs to:
Maths
Time and Work
Question #2
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A can complete a work in 25 days and B in 25 days. If both work together, in how many days will the work be completed?
Correct Answer: Option A
Explanation:
Combined rate = 1/25 + 1/25. Time = 12.5 days.
Combined rate = 1/25 + 1/25. Time = 12.5 days.
This question belongs to:
Maths
Time and Work
Question #3
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A, B and C can do a work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Correct Answer: Option C
Explanation:
Total work = LCM(20, 30, 60) = 60 units. Efficiency of A = 3, B = 2, C = 1. Day 1: A works (3 units). Day 2: A works (3 units). Day 3: A, B, and C work together (3 + 2 + 1 = 6 units). Total work in 3 days = 3 + 3 + 6 = 12 units. To complete 60 units, number of 3-day cycles needed = 60 / 12 = 5 cycles. Total days = 5 * 3 = 15 days.
Total work = LCM(20, 30, 60) = 60 units. Efficiency of A = 3, B = 2, C = 1. Day 1: A works (3 units). Day 2: A works (3 units). Day 3: A, B, and C work together (3 + 2 + 1 = 6 units). Total work in 3 days = 3 + 3 + 6 = 12 units. To complete 60 units, number of 3-day cycles needed = 60 / 12 = 5 cycles. Total days = 5 * 3 = 15 days.
This question belongs to:
Maths
Time and Work
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