Question

A hostel has a provision for 225 students for 40 days. After 15 days, 25 more students join the hostel. How long will the provision last at the same rate?

• A. 26.5 days
• B. 32.5 days
• C. 24.5 days
• D. 22.5 days

Answer 1

The correct option is D 22.5 days

Given, 225 students have provisions for 40 days.

After 15 days,
Provisions for 225 students will last for (40 - 15) = 25 days.
and, the number of students = 225 + 25 = 250.

We know that, if the number of students increases, then, the number of days for which the provision lasts will decrease.

$\text{So, Number of students}\left(x\right)\propto \frac{1}{\text{Number of days}\left(y\right)}$

$\therefore \frac{x_1}{x_2}=\frac{y_2}{y_1}$

Given,
$x_1=225\text{students}$
$y_1=25\text{days}$
$x_2=250\text{students}$
$\text{and}{y}_2=\text{number of days}$

$\Rightarrow \frac{225}{250}=\frac{y_2}{25}$

$\Rightarrow 225\times 25=250\times y_2$

$\Rightarrow y_2=\frac{225\times 25}{250}=22.5days$

So, the provision will last for 22.5 days.