# 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.

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

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