If $6$ men and $8$ boys can do a piece of work in $10$ days and $26$ men and $48$ boys can do same in $ 2 $ days, the time taken by $15$ men and $20$ boys to do the same type of work will be :

The total work is 10 times (6 men + 8 boys), which also equals 2 times (26 men + 48 boys). Setting them equal gives 60 men + 80 boys = 52 men + 96 boys, which simplifies to 8 men = 16 boys, or 1 man = 2 boys. The total work in boy-equivalents is 60 times 2 + 80 = 200 boy-days. For 15 men and 20 boys, their daily capacity is 30 boys + 20 boys = 50 boys, so the time taken is 200 divided by 50, which is 4 days.

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