Question
βPβ and βQβ can complete a task in 72 days,
while βQβ and βRβ can finish 60% of the same task in 27 days. If βRβ is twice as efficient as βPβ, how many days will βRβ alone take to complete the entire task?Solution
Time taken by βQβ and βRβ to do the whole work = (27 Γ 100) / 60 = 45 days Let total work = LCM of 72 and 45 = 360 units Efficiency of βPβ and βQβ = 360 / 72 = 5 units/day Efficiency of βQβ and βRβ = 360 / 45 = 8 units/day Let efficiency of βPβ = y Then efficiency of βRβ = 2y ATQ, (Q + R) - (P + Q) = 2y - y = y = 3 β y = 3 β Rβs efficiency = 2 Γ 3 = 6 units/day Time taken by βRβ = 360 / 6 = 60 days
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