Question
βPβ and βQβ can complete a project in 45 days
and 60 days respectively while βPβ, βQβ and βRβ together can complete the same project in 15 days. Find the time taken by βRβ alone to complete 50% of the work.Solution
ATQ Let total amount of work = 180 units (LCM of 45 and 60) Amount of work done by βPβ in one day = 180/45 = 4 units Amount of work done by βQβ in one day = 180/60 = 3 units Amount of work done by βPβ, βQβ and βRβ in one day = 180/15 = 12 units Amount of work done by βRβ in one day = 12 β 4 β 3 = 5 units Desired time = (0.50 Γ 180)/5 = 18 days
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