Question

In 25 days, one-fifth work is done by 10 men. If the number of days taken to complete three-fifth of the work is 75 days, then how many men were engaged?

• A. 11 men
• B. 12 men
• C. 10 men
• D. 8 men

Answer 1

The correct option is C 10 men

Here, the number of days is inversely proportional to the number of men and directly proportional to the amount of work done.

Number of days	Amount of work done	Number of men
25	$\frac{1}{5}$	10
75	$\frac{3}{5}$	$x$
25 : 75 = 1 : 3	$\frac{1}{5}:\frac{3}{5}$	10 : $x$

Number of men $\propto \frac{1}{Numberofdays}$
$\Rightarrow 10:x=3:1$ ...(i)

Amount of work $\propto$ Number of men
$\Rightarrow \frac{1}{5}:\frac{3}{5}=10:x$ ...(ii)

From (i) and (ii)
10 : $x$
$=\text{compound ratio of}3:1\text{and}\frac{1}{5}:\frac{3}{5}$
$\Rightarrow 10:x=(3:1)\times (\frac{1}{5}:\frac{3}{5})$
$\Rightarrow 10:x=(3\times \frac{1}{5}):(1\times \frac{3}{5})$
$\Rightarrow 10:x=(\frac{3}{5}:\frac{3}{5})$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times \frac{3}{5}=10\times \frac{3}{5}$
$\Rightarrow x=10$

So, ten men were engaged.