A part of monthly hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess. When Swati takes food for 20 days she has to pay \( ₹ 3000 \) as hostel charges whereas Mansi who takes food for 25 days pays \( ₹ 3500 \) as hostel charges. Find the fixed charges and the cost of food per day.

Question

14.A part of monthly hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess. When Swati takes food for 20 days she has to pay \( ₹ 3000 \) as hostel charges whereas Mansi who takes food for 25 days pays \( ₹ 3500 \) as hostel charges. Find the fixed charges and the cost of food per day.

Answer 1

Let the fixed charge be x and the charge/day be y

\(\therefore\) x+ 20y = 3000 , x + 25y = 3500  ......(1)

\(\Rightarrow\) x = 3000 - 20y

Using x's value in equation(1)

3000 - 20y + 25y = 3500

\(\Rightarrow\) 5y = 500 

\(\Rightarrow\) y = 100

\(\therefore\) x = 3000 - 20 \(\times 100\)

\(\Rightarrow\) x = 1000