Question

A hostel has a week's ration for 180 students. For how many days will the ration last, if 30 more students join the hostel?

• A. 6 days
• B. 5 days
• C. 3 days
• D. 4 days

Answer 1

The correct option is A 6 days

Given,
180 students will consume the ration in one week or 7 days.

We know that more is the number of students in the hostel, lesser will be the number of days for which the ration will last.

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

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

Given,
$x_1=180\text{students}$
$y_1=7\text{days}$
$x_2=180+30=210\text{students}$
$y_2=\text{No. of days the ration will last}\text{for 210 students}$

$\Rightarrow \frac{180}{210}=\frac{y_2}{7}$
$\Rightarrow y_2=\frac{180\times 7}{210}=6\text{days}$

So, the number of days for which the ration will last for 210 students = 6 days.