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 = ‘M’ units/day Let the efficiency of a woman = ‘W’ units/day ATQ; (1M + 3W) × 18 = (3M + 2W) × 12 Or, 18M + 54W = 36M + 24W Or, 36M + 108W – (36M + 24W) = 36M + 24W Or, 60W = 36M Or, W:M = 3:5 So, let the efficiency of a woman and a man be ‘3x’ units/day and ‘5x’ units/day, respectively So, total work = (5x + 3 × 3x) × 18 = ‘252x’units Combined efficiency of 5 men and 1 women = (5 × 5x + 3x) = ‘28x’ units/day So, time taken by 5 men and 1 women together to complete the work = 252x ÷ 28x = 9 days