Question

There are 125 students in a hostel. Food provisions for them is for 16 days. How long will these provisions last, if 25 students leave the group?

Answer 1

Here is your answer
125 Students Food last for = 16 days

1 Student Food last for = 16 × 125 days

100 Students last for =
$= \frac{16 \times 125}{100} \\ = 4 \times 5 \\ = 20 \: days$
Hope it helps

Answer 2

Given: Number of students in the hostel = 125

           Food provision for them is for 16 days

To find: How long will the provision last if 25 students leave the group

Let: The provision lasts for $x$ days if 25 students leave the group

Solution: According to the given question and assumption made,

With 125 students in the hostel, food provision lasts for 16 days and,

If 25 students leave the group i.e. with 125 - 25 = 100 students, the provision lasts for $x$ days.

The food provision will last longer than 16 days with less number of students.

So, this is a case of inverse proportion.

∴ $125 \ * \ 16 = 100 \ * \ x$

⇒ $100x = 2,000$

⇒ $x = \frac{2,000}{100} = 20$

Hence, the food provision will last for 20 days, if 25 students leave the group.