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)30
(b)42
(c)48
(d)90
Answer
Answer (as printed): B
Explanation
$$\begin{aligned} 1 \text { man } \equiv & 2 \text { boys } \Leftrightarrow(12 \text { men }+18 \text { boys }) \\ & \equiv(12 \times 2+18) \text { boys }=42 \text { boys. } \end{aligned}$$ Let required number of boys $=x$. 21 men $+x$ boys $\equiv(21 \times 2+x)$ boys $=(42+x)$ boys. Less days, More boys (Indirect Proportion) More hrs per day, Less boys (Indirect Proportion) More work, More boys (Direct Proportion) Days Hours per day Work $$\left.\begin{array}{l} 50: 60 \\ 9: \frac{15}{2} \\ 1: 2 \end{array}\right\}:: 42:(42+x)$$ $\therefore \quad[50 \times 9 \times 1 \times(42+x)]=\left(60 \times \frac{15}{2} \times 2 \times 42\right)$ $\Leftrightarrow \quad(42+x)=\frac{37800}{450} \Leftrightarrow 42+x=84 \Leftrightarrow x=42$.
Explanation as extracted from the printed page; notation may be imperfect.