Question
A can complete a piece of work in 12 days and B can
complete the same work in 18 days. They work together for 4 days and then leave the remaining work to C, who finishes it in 6 days. In how many days can C alone complete the entire work?Solution
Assume total work = LCM of 12 and 18 = 36 units A’s 1-day work = 36/12 = 3 units B’s 1-day work = 36/18 = 2 units (A + B)’s 1-day work = 3 + 2 = 5 units Work done in first 4 days: = 5 × 4 = 20 units Remaining work = 36 − 20 = 16 units Let C’s 1-day work = x units C finishes 16 units in 6 days: 6x = 16 x = 16/6 = 8/3 units per day Time taken by C to complete full work: = 36 / (8/3) = 36 × (3/8) = 108 / 8 = 13.5 days
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