Question

A fort has a provision for 20 days for 200 men. If 50 more men joined the fort, then for how long will the provision last?

• A. 15 days
• B. 19 days
• C. 18 days
• D. 16 days

Answer 1

The correct option is D 16 days

Given,
For 200 men, the provision will last for 20 days.

We know that if the number of men increase, the provision will last for lesser days.

$\text{So, Number of men}\left(x\right)\propto \frac{1}{\text{Number of days}\left(y\right)}$
$\therefore \frac{x_1}{x_2}=\frac{y_2}{y_1}$

Given,
$x_1=200\text{men}$
$y_1=20\text{days}$
$x_2=200+50=250\text{men}$
$\text{and}{y}_2=\text{no. of days for which}\text{the provision will last for 250 men}$

$\Rightarrow y_2=\frac{x_1\times y_1}{x_2}$
$\Rightarrow y_2=\frac{200\times 20}{250}=16\text{days}$

Hence, the provision will last for 16 days if 50 more men joined the fort.