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3 men can complete a work (amount = W) in 40 days. So,
1 man can complete W in 40 * 3 days = 120 days.
Work per day of 1 man = capacity of 1 man = \frac{1}{120} of W per day

6 boys can complete W in 40 days. Similarly, we get,
work per day of 1 boy = \frac{1}{240} of W

Work per day by 6 men and 8 boys =
    \frac{6}{120}\ W + \frac{8}{ 240}\ W\ = \frac{20}{240}\ of\ W = \frac{1}{12} of W

So, 6 men and 8 boys can complete work W in : \frac{W}{\frac{1}{12} W} = 12 days