Question
A work can be completed by ‘A’ and ‘B’, alone in
12 days and 14 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 3 days.Solution
Let total work = 84 units (LCM of 12 and 14) Efficiency of ‘A’ = (84/12) = 7 units/day Efficiency of ‘B’ = (84/14) = 6 units/day Combined efficiency of ‘A’, ‘B’ and ‘C’ = (84/3) = 28 units/day Efficiency of ‘C’ = 28 – (7 + 6) = 15 units/day Required time taken = (84/15) = 5.6 days
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