Question

A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student $A$ takes food for $20$ days, he has to pay Rs. $1000$ as hostel charges whereas a student $B$, who takes food for $26$ days, pays Rs. $1180$ as hostel charge. Find the fixed charge in Rs

Answer 1

Let the fixed charges = y (in rupees) and the cost of food per day = x (in rupees).

Now, A takes food for 20 days and pays Rs. 1000.

That is, 20x+y=1000 .................(1)

Also, B takes food for 26 days and pays Rs. 1180.

That is, 26x+y=1180 ..................(2)

Subtracting (1) from (2), we get,

6x=180

i.e. x =30

Substitute x=30 in (1), we get,

20(30)+ y=1000

i.e. 600 +y=1000

i.e. y = 400

Hence, the fixed charges are Rs. 400 and the cost of food per day is Rs. 30.