Question
Mohan, Sohan, and Rohan alone can finish a piece of work
in 50, 100, and 150 days respectively. They start the work together, but Mohan leaves after 8 days and Sohan leaves 14 days after Mohan. How long did Rohan work?Solution
Total work = LCM of 50, 100, and 150 = 300 units. Mohan's daily work = 300/50 = 6 units. Sohan's daily work = 300/100 = 3 units. Rohan's daily work = 300/150 = 2 units. Work done in the first 8 days = 8 × (6 + 3 + 2) = 88 units. Work done by Sohan and Rohan together in the next 14 days = 14 × (3 + 2) = 70 units. Remaining work = 300 - 88 - 70 = 142 units. Time taken by Rohan to complete the remaining work = 142/2 = 71 days. Total days Rohan worked = 8 + 14 + 71 = 93 days.
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