A hostel has provisions for 200 students for 30 days. If 100 new students join the hostel, the same provisions will last for:

1. 45 days

2. 30 days

3. 60 days

4. 20 days

Original no. of students in hostel = 200

New no. of students in hostel = 200 + 100 = 300

For 300 students, let the provisions last for x days.

Since it is a case of inverse variation,

$\therefore 200 \times 30 = 300 \times x\\[1em] \Rightarrow 6000 = 300x\\[1em] \Rightarrow x = \dfrac{6000}{300}\\[1em] \Rightarrow x = 20$

Hence, option 4 is the correct option.