Q15 of 186 Page 4

A part of monthly hostel charges in a college 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. 1750 as hostel charges whereas a student a d who takes food for 28 days, pays Rs. 1900 as hostel charges. Find the fixed charges and the cost of the food per day.

Let fixed hostel charge (monthly) = Rs x

and cost of food for one day = Rs y


In case of student A,


x + 25y = 1750 …(i)


In case of student B,


x + 28y = 1900 …(ii)


On subtracting Eq. (i) from Eq. (ii), we get


x + 28y – x – 25y = 1900 – 1750


⇒ 3y = 150


⇒ y = 50


On putting the value of y = 50 in Eq. (i), we get


x + 25(50) = 1750


⇒ x + 1250 = 1750


⇒ x = 1750 – 1250 = 500


Hence, monthly fixed charges is Rs. 500 and cost of food per day is Rs. 50


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