Q13 of 186 Page 4

A part of monthly hostel charges in a college is fixed and the remaining depend on the number of days one has taken food in the mess. When a student A, takes food for 22 days, he has to pay Rs. 1380 as hostel charges, whereas a student B, who takes food for 28 days, pays Rs. 1680 as hostel charges. Find the fixed charge and the cost of 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 + 22y = 1380 …(i)


In case of student B,


x + 28y = 1680 …(ii)


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


x + 28y – x – 22y = 1680 – 1380


⇒ 6y = 300


⇒ y = 50


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


x + 22(50) = 1380


⇒ x + 1100 = 1380


⇒ x = 1380 – 1100 = 280


Hence, monthly fixed charges is Rs. 280 and cost of food per day is Rs. 50


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