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.
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