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. 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 = 4550   ...(i)

x + 30y = 5200   ...(ii)

Subtracting (i) from (ii), we get

(x + 30y) – (x + 25y) = 5200 – 4550

5y = 650 

⇒ `y = 650/5`

⇒ y = 130

Now, putting y = 140, we have

x + 25 × 130 = 4550

x + 3250 = 4550

⇒ x = 4550 – 3250 

⇒ x = 1300

Hence, the fixed charges be Rs. 1300 and the cost of the food per day is Rs. 130.