Question
P, Q, and R can do a project individually in 10, 25, and
20 days. P and Q begin the project, but after 2 days, P is replaced by R. How many more days will Q and R need to finish the project?Solution
ATQ,
Total work = LCM of (10, 25, 20) = 100 units P’s efficiency = 100 ÷ 10 = 10 units/day Q’s efficiency = 100 ÷ 25 = 4 units/day R’s efficiency = 100 ÷ 20 = 5 units/day First 2 days: (10 + 4) × 2 = 28 units done Remaining = 100 - 28 = 72 units Q and R = (4 + 5) = 9 units/day Let x = number of days needed So, 9x = 72 → x = 8 Therefore, Q and R together will need 8 days to finish the rest.
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