Given ,6 men and 8 boys can complete the task in 10 days, and 26 men and 48 boys can finish it in just 2 days, how long will it take for 15 men and 20 boys to do the same work?
4 days
Let one man's one-day work be \(m\) and one boy's one-day work be \(b\).
The total work is the same both times: \((6m+8b)\times 10 = (26m+48b)\times 2\).
This gives \(60m+80b = 52m+96b\), so \(8m = 16b\) and \(m = 2b\).
Express the work in boy-units: \(6m+8b = 6(2b)+8b = 20b\).
So total work \(= 20b\times 10 = 200b\) boy-days.
The new group does \(15m+20b = 15(2b)+20b = 50b\) per day.
Time required \(= \dfrac{200b}{50b} = 4\) days.
15 men and 20 boys will take 4 days.
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