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


Option B


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)

$\left\{\begin{array}{c}Work\quad 1:2\\ Speed\quad \frac{1}{3}:\frac{1}{2}\end{array}\right\}::25:x$

$\therefore\left(1\times\frac{1}{3}\times x\right)$ $=\left(2\times\frac{1}{2}\times 25\right)$

$\Leftrightarrow x=75$