Question

The ratio of the amount of work done by 'x' men in 5 days and 'x+10' men in '2x-5' days is 1:3.
The value of x =

• A. 10
• B. 50
• C. 25
• D. 5

Answer 1

The correct option is D 5

Assuming that all men do the same amount of work in one day and one day work for each men = 1 unit.

$\Rightarrow$ Amount of work done by x men in 5 days
= Amount of work done by 5x men in one day.
=5x units of work.
Similarly,
$\Rightarrow$ Amount of work done by (x+10) men in (2x-5)
=(x+10)(2x-5) units of work.

According to the give information, we get,
$\Rightarrow \frac{5x}{(x+10)(2x-5)}=\frac{1}{3}$
$\Rightarrow 15x=(x+10)(2x-5)$
$\Rightarrow 15x=2x^2-5x+20x-50$
$\Rightarrow 15x=2x^2+15x-50$
$\Rightarrow 0=2x^2-50$
$\Rightarrow 2x^2=50$
$\Rightarrow x^2=25$
$\Rightarrow x=\pm 5$
$\because \text{Number of men cannot be -ve, we get}$
$x=5$