A part of monthly hostel charges in a college hostel are 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, has to pay Rs.5200. Find the fixed charges per month and the cost of the food per day.

Question

Philoid · Accepted Answer

Let the per day fixed charge of hostel be x.

Excluding fixed charge, a student pays Rs. (4500 - 30x) for 25 days and Rs. (5200 - 30x) for 30 days mess charge

Cost of food per day is given by -

On Cross multiplying, we get -

⇒ 30(4500 - 30x) = 25(5200 - 30x)

⇒ 135000 - 900x = 130000 - 750x

⇒ 150x = 5000

⇒ x = (500/15)

Hence, the fixed charge of hostel per month = (500/15)×30 = Rs. 1000

and, Rate per km = ((4500 - 1000)/25) = (3500/25) = Rs. 140