Question
Mike and Jenny alone can complete a task in 24 days and
40 days respectively. They aim to finish the work in 'd' days. What percentage increase in Jenny's efficiency is required for them to finish the work in 'd/2' days?(Can calculate approx. value)Solution
ATQ, Total work = LCM of 24 and 40 = 120 units Efficiency of Mike = 120 / 24 = 5 units/day Efficiency of Jenny = 120 / 40 = 3 units/day Combined efficiency = 5 + 3 = 8 units/day Original time (d) = 120 / 8 = 15 days Required time (d/2) = 7.5 days Required total efficiency = 120 / 7.5 = 16 units/day Increase needed for Jenny = 16 - 5 = 11 units/day Percentage increase = ((11 - 3) / 3) × 100 = 266.67% or 267%
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