Q. 273.9( 7 Votes )

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.

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


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