Question
βPβ alone can paint a house in 18 days, while
βPβ and βQβ together can do it in 12 days. If βQβ started the work and left after 6 days, how many days will βPβ take to complete the painting?Solution
ATQ,
Let the total work = 36 {L.C.M of 18 and 12}
Efficiency of βPβ = 36 Γ· 18 = 2 units/day
Combined efficiency of βPβ and βQβ = 36 Γ· 12 = 3 units/day
So, efficiency of βQβ alone = 3 β 2 = 1 unit/day
Work done by βQβ in 6 days = 1 Γ 6 = 6 units
Remaining work = 36 β 6 = 30 units
Time taken by βPβ alone = 30 Γ· 2 = 15 days
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