There are 1200 students in a hostel. If the number of students is increased by 300, then the expenses of the mess increase by ₹5,000 per day, while the average expenditure per head diminishes by ₹5. The original expenditure of the mess,per day,is:

Let's assume the original expenditure of the mess per day is 'y'.

There are 1200 students in a hostel.

average original expenditure of the mess = $$\frac{y}{1200}$$    Eq.(i)

If the number of students is increased by 300, then the expenses of the mess increase by ₹5,000 per day.

average expenditure of the mess after the increase in the number of students = $$\frac{y+5000}{1200+300}$$

= $$\frac{y+5000}{1500}$$    Eq.(ii)

while the average expenditure per head diminishes by ₹5.

Eq.(i) = Eq.(ii) + 5

$$\frac{y}{1200} = \frac{y+5000}{1500} + 5$$

$$\frac{y}{1200} = \frac{y+5000+7500}{1500}$$

$$\frac{y}{4} = \frac{y+12500}{5}$$

5y = 4y+50000

5y-4y = 50000

original expenditure of the mess per day = y = 50000