12 men and 18 boys, working $7\frac{1}{2}$ hours a day, can do a piece of work in 60 days. If a man works equal to 2 boys, then how many boys will be required to help 21 men to do twice the work in 50 days, working 9 hours a day ?

A) 59

B) 40

C) 42

D) 48


Option C


$1$ man = $2$ boys  $\Rightarrow$ ($12$ men + $18$ boys) $=(12\times 2+18)$ boys = 42 boys

Let required number of boys $= x$.

$21$ men + $x$ boys $=(21\times 2+x)$ boys $=(42+x)$ boys

Less days, More boys (Indirect Proportion)

More hrs per day, Less boys (Indirect Proportion)

$\left\{\begin{array}{c}Days\quad\quad\quad 50:60\\ Hours/Day\quad 9:\frac{15}{2}\\Work\quad\quad\quad\quad 1:2\end{array}\right\}::42:(42+x)$

$\therefore [50\times 9\times 1\times(42+x)]$ $=\left(60\times \frac{15}{2}\times 2\times 42\right)$

$\Leftrightarrow (42+x)$ $=\frac{37800}{450}$

$\Leftrightarrow 42+x=84$ 

$\Leftrightarrow x=42$.