Question

A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes food for 20 days, he has to pay ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charge and the cost of food per day.

Answer 1

Given: Let fixed monthly charge = ₹ x and cost of food per day = ₹ y.

Step-wise calculation:

1. From student A:

x + 20y = 1000

2. From student B:

x + 26y = 1180

3. Subtract (1) from (2):

(x + 26y) – (x + 20y) 

= 1180 – 1000

⇒ 6y = 180

⇒ y = 30

4. Substitute y = 30 into (1):

x + 20(30) = 1000

⇒ x + 600 = 1000

⇒ x = 400

Fixed charge = ₹ 400 per month.

Cost of food = ₹ 30 per day.