Question
Worker ‘P’ can finish a task in 54 days, which is 18
days quicker than worker ‘Q’. If they take turns daily starting with ‘P’, find the total time (in days) to complete the task.Solution
ATQ,
Time taken by 'Q' = 54 + 18 = 72 days Let total work be 216 units (LCM of 54 and 72) Efficiency of 'P' = 216 ÷ 54 = 4 units/day Efficiency of 'Q' = 216 ÷ 72 = 3 units/day Work in 2 days = 4 + 3 = 7 units Work in 60 days = 7 × 30 = 210 units Remaining work = 216 - 210 = 6 units Time by 'P' to finish remaining = 6 ÷ 4 = 1.5 days Hence, final Answer: 60 + 1.5 = 61.5 days
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