Question
A work can be completed by ‘A’ and ‘B’, alone in 15 days and 10 days, respectively. Find the number of days taken by ‘C’ to complete the same work alone if ‘A’, ‘B’ and ‘C’ together can complete the whole work in 4 days.
Solution
Let total work = 30 units (LCM of 15 and 10) Efficiency of ‘A’ = (30/15) = 2 units/day Efficiency of ‘B’ = (30/10) = 3 units/day Combined efficiency of ‘A’, ‘B’ and ‘C’ = (30/4) = 7.5 units/day Efficiency of ‘C’ = 7.5 – (2 + 3) = 2.5 units/day Required time taken = (30/2.5) = 12 days
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