Question
A task can be completed in 10 days by a team of 6 men
and 8 boys. The same task can also be completed in 2 days by 26 men and 48 boys. How long will it take for a group consisting of 15 men and 20 boys to complete the same task?Solution
Let efficiency of a men and a boy is ‘x’ units per day and ‘y’ units per day.
According to question:
(6x + 8y) × 10 = (26x + 48y) × 2
30x + 40y = 26x + 48y
4x = 8y
x = 2y
Total work = (6x + 8y) × 10 = 20y × 10 = 200y units
Efficiency of 15 men and 20 boys = 15x + 20y = 50y per day
Require time = 200y/50y = 4 days
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