20 men complete one-third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days?
(a)10
(b)12
(c)15
(d)20
Answer
Answer (as printed): B
Explanation
Let the total number of men be $x$. Work done $= \frac{1}{3}$, Remaining work $= \left(1-\frac{1}{3}\right) = \frac{2}{3}$. More work, More men (Direct Proportion). More days, Less men (Indirect Proportion). Work $\frac{1}{3}:\frac{2}{3}$, Days $25:20$ :: $20:x$. $\therefore \frac{1}{3} \times 25 \times x = \frac{2}{3} \times 20 \times 20 \Leftrightarrow x = \frac{800}{25} = 32$. $\therefore$ More men to be employed $= (32-20) = 12$.
Explanation as extracted from the printed page; notation may be imperfect.