Question

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.

Answer 1

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