Question
A work can be completed by βAβ and βBβ, alone in
10 days and 15 days, respectively. Find the number of days taken by βCβ to complete the same work alone if βAβ, βBβ and βCβ together can complete the whole work in 3 days.Solution
Let total work = 30 units (LCM of 10 and 15) Efficiency of βAβ = (30/10) = 3 units/day Efficiency of βBβ = (30/15) = 2 units/day Combined efficiency of βAβ, βBβ and βCβ = (30/3) = 10 units/day Efficiency of βCβ = 10 β (3 + 2) = 5 units/day Required time taken = (30/5) = 6 days
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