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.

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.