Question

A hostel has ration for 50 days for 80 students. A certain number of students joined the hostel and the ration lasted for only 40 days. How many students joined the hostel?

• A. 25
• B. 20
• C. 50
• D. 10

Answer 1

The correct option is B 20

Given, the ration will last for 50 days if 80 students were there.

We know that if the ration lasts for fewer days, there is an increase in the number of students in the hostel.

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

Given,
$x_1=50days$
$y_1=80students$
$x_2=40days$
$\text{and}{y}_2=\text{Total number of students}$
$\Rightarrow y_2=\frac{x_1\times y_1}{x_2}$
$\Rightarrow y_2=\frac{50\times 80}{40}=100$

So, the number of students that joined = 100 - 80 = 20