A can do a work in 20 days and B in 30 days. They work together for 7 days and then both leave. Then C alone finishes the remaining work in 10 days. In how many days will C alone finish the whole work?
Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. Combined efficiency = 5 units/day. In 7 days, work done = 7 * 5 = 35 units. Remaining work = 60 - 35 = 25 units. C's efficiency = 25 units / 10 days = 2.5 units/day. Days for C to complete total work = 60 / 2.5 = 24 days.
A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days can A and B together complete the work?
Explanation:
Let total work be 80 units. Efficiency of A = 1 unit/day. In 10 days, A completes 10 units. Remaining work = 80 - 10 = 70 units. B finishes 70 units in 42 days, so B's efficiency = 70 / 42 = 5/3 units/day. Combined efficiency of A and B = 1 + 5/3 = 8/3 units/day. Time taken together = 80 / (8/3) = (80 * 3) / 8 = 30 days.
A can do a piece of work in 25 days and B can finish it in 20 days. They work together for 5 days and then A leaves. In how many days will B finish the remaining work?
Explanation:
Total work = LCM(25, 20) = 100 units. Efficiency of A = 4, B = 5. Combined efficiency = 9 units/day. In 5 days, work done = 5 * 9 = 45 units. Remaining work = 100 - 45 = 55 units. Time taken by B to complete remaining work = 55 / 5 = 11 days.
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