Question
A work can be completed by βAβ and βBβ, alone in
14 days and 7 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 2 days.Solution
Let total work = 14 units (LCM of 14 and 7) Efficiency of βAβ = (14/14) = 1 units/day Efficiency of βBβ = (14/7) = 2 units/day Combined efficiency of βAβ, βBβ and βCβ = (14/2) = 7 units/day Efficiency of βCβ = 7 β (1 + 2) = 4 units/day Required time taken = (14/4) = 3.5 days
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