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 25days, he has to pay Rs. 4550 as hostel charges whereas a student B, who takes food for 30 days, pays Rs. 5200 as hostel charges. Find the fixed charges and the cost of the food per day.

Answer 1

Let the fixed charges be Rs.x and the cost of food per day be Rs.y.
Then as per the question
x + 25y = 4500                      ………(i)
x + 30y = 5200                      ……..(ii)
Subtracting (i) from (ii), we get
5y = 700 ⇒ y = `700/5` = 140
Now, putting y = 140, we have
x + 25 × 140 = 4500
⇒x = 4500 – 3500 = 1000
Hence, the fixed charges be Rs.1000 and the cost of the food per day is Rs.140.