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 $\displaystyle 20$ days, she has to pay ₹ $\displaystyle 1,500$ as hostel charges while another student B, who takes food for $\displaystyle 26$ days, pays ₹ $\displaystyle 1,800$ . Find the fixed charges and the cost of food.

Let the monthly fixed charges of hostel be ₹ x and cost of food be ₹ y per day. A.T.Q \[\begin{array}{ll} \mathrm{x}+20 \mathrm{y}=1500 & -\ldots-\ldots-(\mathrm{i}) \\ \mathrm{x}+26 \mathrm{y}=1800 & -\ldots-\ldots-\ldots(\text { ii }) \end{array} \] Solving equations (i) & (ii) \[x=500, y=50 \] Hence, the monthly fixed charges of hostel be ₹ $\displaystyle 500$ and cost of food be ₹ $\displaystyle 50$ per day.