Question
P can complete a work in 25 days, while Q can complete
the same work in 30 days. They work together for 5 days, and then P is replaced by R, who can complete the work in 40 days. In how many more days will the remaining work be completed?Solution
Let the total work be 1 unit. P’s efficiency = 1/25, Q’s efficiency = 1/30, and R’s efficiency = 1/40. Work done by P and Q in 5 days = (1/25 + 1/30) × 5 = (11/150) × 5 = 11/30. Remaining work = 1 - 11/30 = 19/30. Now, Q and R are working together. Their combined efficiency = 1/30 + 1/40 = 7/120. Time taken to complete the remaining work = (19/30) ÷ (7/120) = 76/7 ≈ 11 days. Final Answer: (a) 11 days
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