A can complete a work in 12 days and B can complete the same work in 22 days. If they work together, in how many days will the work be completed? MCQ with Answer and Explanation
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?
Explanation:
Total work = LCM(10, 15, 20) = 60 units. Efficiency of A = 6, B = 4, C = 3. A and C work for 2 days: work done = 2 * (6 + 3) = 18 units. Remaining work = 60 - 18 = 42 units. B and C complete remaining work together with efficiency = 4 + 3 = 7 units/day. Time taken for remaining work = 42 / 7 = 6 days. Total time = 2 + 6 = 8 days.
A, B and C can do a piece of work in 20, 30 and 60 days respectively. If A works everyday and is assisted by B and C together on every third day, then in how many days will the work be completed?
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+C work = 3 + 2 + 1 = 6 units. Work done in 3 days = 3 + 3 + 6 = 12 units. Number of 3-day cycles to complete 60 units = 60 / 12 = 5 cycles. Total days = 5 * 3 = 15 days.
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