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

A. 4 days

B. 5 days

C. 6 days

D. 7 days

Solution:

\begin{aligned} Let 1 man's 1 day's work = x and \\ 1 boy's 1day's work = y \\ Then, 6 x + 8 y = \frac{1}{10} and \\ 26 x + 48 y = \frac{1}{2} \\ Solving these two equations, we get \\ x = \frac{1}{100} a n d y = \frac{1}{200} \\ (15 men + 20 boy)'s 1 day's work \\ = \frac{15}{100} + \frac{20}{200} = \frac{1}{4} \\ ∴ 15 men and 20 boys can do the work in 4 days \end{aligned}

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