Question
When one man and three women work together, they need 18
days to finish a task. On the other hand, when three men and two women collaborate, they can complete the same task in 12 days. Now, let's determine the amount of time required for five men and one woman to work together to complete the task.Solution
According to questions Let the efficiency of a man = βMβ units/day Let the efficiency of a woman = βWβ units/day ATQ; (1M + 3W) Γ 18 = (3M + 2W) Γ 12 Or, 18M + 54W = 36M + 24W Or, 36M + 108W β (36M + 24W) = 36M + 24W Or, 60W = 36M Or, W:M = 3:5 So, let the efficiency of a woman and a man be β3xβ units/day and β5xβ units/day, respectively So, total work = (5x + 3 Γ 3x) Γ 18 = β252xβunits Combined efficiency of 5 men and 1 women = (5 Γ 5x + 3x) = β28xβ units/day So, time taken by 5 men and 1 women together to complete the work = 252x Γ· 28x = 9 days
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