Question

A hostel had rations for 60 days for 500 students. After 12 days, 300 more students join the hostel. How long will the remaining rations last?

Answer 1

Hint: The given question is based on the proportionality concept. With the help of problem statements first try to find out if the problem consists of direct variation or inverse variation. Further proceed with the formula for the type of variation.

Complete step-by-step answer:
Let the number of days X
After 12 days, for 500 students the food would last for $60-12=48$ days
Now, we have
Number of students increased to 800 then the number of days for the food last is x.

When the number of students increases, the food would last for fewer days.
Thus, there is inverse variation between students and number of days.
$$\begin{gathered} \Rightarrow 500\times 48=800\times x \\ \Rightarrow x={\displaystyle \frac{500\times 48}{800}}=30 \end{gathered}$$
Thus, the food will last for $30$ days.

Note: The given question is based on the proportionality concept. To solve these types of questions remember the concept of direct proportion and indirect proportion. Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent. Two quantities are said to be indirectly proportional, if on the increase of the one, the other decreases to the same extent and vice-versa.