Solution:
1 man ≡ 2 boys ⇔ (12 men + 18 boys)
≡ (12 × 2 ×18) boys = 42 boys
Let required number of boys = x
⇒ (21 men + x boys) ≡ (21 × 2 × x) boys = (42 + x) boys
Less days, More boys (Indirect proportion)
More hours per day, Less boys (Indirect proportion)
More work, More boys (Direct proportion)
\[\left. \begin{gathered}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 50}}:60 \hfill \\
{\text{Hours per day 9}}:\frac{{15}}{2} \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Work }}1:2 \hfill \\
\end{gathered} \right\}::42:\left( {42 + x} \right)\]
$$\therefore \left[ {50 \times 9 \times 1 \times \left( {42 + x} \right)} \right] = $$ $$\left( {60 \times \frac{{15}}{2} \times 2 \times 42} \right)$$
$$\eqalign{
& \Leftrightarrow \left( {42 + x} \right) = \frac{{37800}}{{450}} \cr
& \Leftrightarrow 42 + x = 84 \cr
& \Leftrightarrow x = 42 \cr} $$