If 3 men or 6 boys can do a piece of work in 10 days, working 7 hours a day; how many days will it take to complete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day?
(a)6
(b)$7 \frac{1}{2}$
(c)$8 \frac{1}{2}$
(d)9
Answer
Answer (as printed): B
Explanation
3 men $\equiv 6$ boys ⇔ (6 men + 2 boys) $\equiv 14$ boys. More work, More days (Direct Proportion) More boys, Less days (Indirect Proportion) More hours per day, Less days (Indirect Proportion) Work Hours per day $$\left.\begin{array}{r} 1: 2 \\ 14: 6 \\ 8: 7 \end{array}\right\}:: 10: x$$ $\therefore(1 \times 14 \times 8 \times x)=(2 \times 6 \times 7 \times 10)$ $\Leftrightarrow x=\frac{840}{112}=7 \frac{1}{2}$.
Explanation as extracted from the printed page; notation may be imperfect.