Question
The efficiency of a woman is 33.33% less than that of a
man, whose efficiency is three times that of a child. If 2 children, 3 women, and 4 men together can complete a task in 25 days, how many additional men are needed to assist 2 children and 4 women so that the task is completed in 20 days?Solution
Let the efficiency of a man be '3e' units/day. Efficiency of a woman = (2/3) x 3e = '2e' units/day Efficiency of a child = (1/3) x 3e = 'e' units/day Total work = (2 x e + 3 x 2e + 4 x 3e) x 25 = (2e + 6e + 12e) x 25 = 500e units Let required number of men be 'm'. So, (2 x e + 4 x 2e + m x 3e) x 20 = 500e Or, 2 + 8 + 3m = 25 Or, 3m = 15 So, 'm' = 5 Therefore, required number of men are 5
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