2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in :
(a)18 days
(b)21 days
(c)24 days
(d)30 days
Answer
Answer (as printed): B
Explanation
$$\begin{aligned} & (2 \times 14) \text { men }+(7 \times 14) \text { boys } \\ & \\ & \equiv(3 \times 11) \text { men }+(8 \times 11) \text { boys } \\ & \Leftrightarrow \quad 5 \text { men } \equiv 10 \text { boys } \Leftrightarrow 1 \mathrm{man} \equiv 2 \text { boys. } \\ & \therefore \quad(2 \text { men }+7 \text { boys }) \equiv(2 \times 2+7) \text { boys }=11 \text { boys. } \end{aligned}$$ Let the required number of days be $x$. Now, More boys, Less days (Indirect Proportion) More work, More days (Direct Proportion) Boys $$\left.\begin{array}{c} 22: 11 \\ 1: 3 \end{array}\right\}:: 14: x$$ $\therefore(22 \times 1 \times x)=(11 \times 3 \times 14)$ $\therefore x=\frac{462}{22}=21$.
Explanation as extracted from the printed page; notation may be imperfect.