Question
A work can be completed by βAβ and βBβ, alone in
18 days and 12 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 4 days.ΒSolution
Let total work = 36 units (LCM of 18 and 12) Efficiency of βAβ = (36/18) = 2 units/day Efficiency of βBβ = (36/12) = 3 units/day Combined efficiency of βAβ, βBβ and βCβ = (36/4) = 9 units/day Efficiency of βCβ = 9 β (2 + 3) = 4 units/day Required time taken = (36/4) = 9 days
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