Question

A part of monthly hostel charges in a college hostel is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25 days, he has to pay Rs.4500, whereas a student B who takes food for 30 days, he has to pay Rs.5200. Find the fixed charges per month and the cost of the food per day.

Answer 1

let the fixed charge be 'x' and the cost of food per day be y.

According to the question, For A it is,
x + 25y = 4500 ------------(1)

and for B it is,
x + 30y = 5200 ------------(2)

By the elemination method,

-5y = -700

... 5y = 700

=> y = $\frac{700}{5}$

=> y = 140

And, substituting the value of y in eq. (1), we get,

=> x + 25 $\times$ 140= 4500

=> x = 4500- 3500

=> x = 1000

Hence, the fixed charge is Rs. 1000 and cost of the food per day is Rs. 140