Question
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?Solution
Let the efficiency of a man be βpβ units per day and the efficiency of a boy be βqβ units per day. According to the question: (6p + 5q) Γ 9 = (24p + 20q) Γ 3 Or, 54p + 45q = 72p + 60q Or, 15q = 18p Or, q = 1.2p Total work = (6p + 5q) Γ 9 = (6p + 6p) Γ 9 = 12p Γ 9 = β108pβ 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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