Question

In a hostel, 75 students had food provision for 24 days. If 15 students leave the hostel, for how many days would the food provision last?

Answer 1

Let x be the required number of days. Then, we have:

No. of students	75	60
No. of days	24	x

Clearly, less number of students will take more days to finish the food.
So, it is a case of inverse proportion.
$$\begin{gathered} \mathrm{Now},75\times 24=60\times x \\ \Rightarrow x=\frac{75\times 24}{60} \\ \Rightarrow x=30 \end{gathered}$$

Therefore, the food will now last for 30 days.