If a certain number of workmen can do a piece of work in 25 hours, in how many hours will another set of an equal number of men, do a piece of work, twice as great, supposing that 2 men of the first set can do as much work in an hour, as 3 men of the second set do in an hour?
(a)60
(b)75
(c)90
(d)105
Answer
Answer (as printed): B
Explanation
Let the required number of hours be $x$. Speeds of working of first and second type of men are $\frac{1}{2}$ and $\frac{1}{3}$. More work, More time (Direct Proportion). Less speed, More time (Indirect Proportion). Work $1:2$, Speed $\frac{1}{3}:\frac{1}{2}$ :: $25:x$. $\therefore \left(1 \times \frac{1}{3} \times x\right) = \left(2 \times \frac{1}{2} \times 25\right) \Leftrightarrow x = 75$.
Explanation as extracted from the printed page; notation may be imperfect.