If 6 men and 5 boys can complete a piece of work in 9 days, while 24 men and 20 boys can complete the same work in 3 days, how long will it take for 12 men and 15 boys to complete the same work?
Let the efficiency of a man be ‘p’ units per day and the efficiency of a boy be ‘q’ units per day. According to the question: (6p + 5q) × 9 = (24p + 20q) × 3 Or, 54p + 45q = 72p + 60q Or, 15q = 18p Or, q = 1.2p Total work = (6p + 5q) × 9 = (6p + 6p) × 9 = 12p × 9 = ‘108p’ units Efficiency of 12 men and 15 boys = 12p + 15q = 12p + 18p = 30p units per day Required time = (108p / 30p) = 3.6 days
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