A and B can complete a work in 12 days and 16 days respectively. Both work together for 3 days and then A leaves. How long will B take to complete the remaining work?
Explanation:
Total work = LCM(12, 16) = 48 units. Efficiency of A = 4, B = 3. Combined efficiency = 7 units/day. In 3 days, work completed = 3 * 7 = 21 units. Remaining work = 48 - 21 = 27 units. Time taken by B to complete remaining work = 27 / 3 = 9 days.
Explanation:
Let efficiency of B = 10, then efficiency of A = 13. Total work = Efficiency of A * Time taken by A = 13 * 23 = 299 units. Combined efficiency of A and B = 13 + 10 = 23. Time taken together = 299 / 23 = 13 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 will A and B together complete the work?
Explanation:
A's 10-day work = 10/80 = 1/8. Remaining work = 7/8. B completes 7/8 work in 42 days, so B completes full work in 42 * (8/7) = 48 days. Combined 1-day work = 1/80 + 1/48 = (3 + 5)/240 = 8/240 = 1/30. They finish together in 30 days.
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