A can finish 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 can C alone finish the full work?
Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. Combined efficiency = 5 units/day. In 7 days, work completed = 7 * 5 = 35 units. Remaining work = 60 - 35 = 25 units. C takes 10 days to do 25 units, so efficiency of C = 25 / 10 = 2.5 units/day. Time taken by C alone for full work = 60 / 2.5 = 24 days.
X can do a piece of work in 40 days. He works at it for 8 days and then Y alone finishes the remaining work in 16 days. How long will X and Y together take to complete the work?
Explanation:
Let total work be 40 units. Efficiency of X = 1 unit/day. In 8 days, X completes 8 units. Remaining work = 40 - 8 = 32 units. Y finishes 32 units in 16 days, so Y's efficiency = 32 / 16 = 2 units/day. Combined efficiency of X and Y = 1 + 2 = 3 units/day. Time taken together = 40 / 3 = 13(1/3) days.
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