A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she 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 charges and the cost of food per day.
₹ 400, ₹ 30
Let 'x' be the fixed monthly charges for the hostel and 'y' be the charge for food per day.
According to the question,
x + 20y = 1000 ... (i)
x + 26y = 1180 ... (ii)
Subtracting equation (i) from equation (ii), we get
6y = 180
Putting this value in equation (i), we get
x + 20 × 30 = 1000
⇒ x = 1000 - 600
⇒ x = 400
Hence, fixed charge = ₹ 400 and charge per day = ₹ 30.