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?

• A. 54 days
• B. 55 days
• C. 60 days
• D. 50 days

Answer 1

The correct option is D 50 days

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.