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.
A and B can complete a piece of work in 12 and 18 days respectively. They begin the work together, but A leaves 4 days before the completion of the work. For how many days did A and B work together?
Explanation:
Total work = LCM(12, 18) = 36 units. Efficiency of A = 3, B = 2. Let total days be x. B works for x days, A works for (x - 4) days. 3(x - 4) + 2x = 36 => 3x - 12 + 2x = 36 => 5x = 48 => x = 9.6 days. A and B worked together for x - 4 = 9.6 - 4 = 5.6 days.
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