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 Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.

Answer 1

Let the fixed charge be 'x' and the cost of food per day be y.

According to the question,

For A, x + 20y = 1000 ----------------(1)

For B, x + 26y = 1180 ------------(2)

Subtracting equation (1) from (2),

6y = 180

$\Rightarrow$ y = 30

Substituting the value of y in eq. (1), we get,

$\Rightarrow$ x + 20 $\times$ 30 = 1000

$\Rightarrow$ x = 1000 - 600

$\Rightarrow$ x = 400

Hence, the fixed charge is Rs. 400 and cost of the food per day is Rs. 30.