Question

In a fort, 200 men had provision for 60 days. After 20 days, 40 men were shifted to other places. How long will the provision last for remaining men at the same rate?

Answer 1

Given, 200 men had provision for 60 days.

After 20 days,
200 men will have that provision for (60 - 20) = 40 days
and, number of men left = 200 - 40 = 160

We know that if the number of men decrease, the provision will last longer.

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

Given,
$x_1=200men$
$y_1=40days$
$x_2=160men$
$\text{and}{y}_2=\text{no. of days for 160 men}$

$\Rightarrow \frac{200}{160}=\frac{y_2}{40}$
$\Rightarrow 200\times 40=160\times y_2$
$\Rightarrow y_2=\frac{200\times 40}{160}=50days$

So, the provision will last for next 50 days for 160 men.