4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(i) 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 Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.
Let x be the fixed charge of the food 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
y = 180/6 = 30
Putting this value in equation (i), we get
x + 20 × 30 = 1000
x = 1000 - 600
x = 400
Hence, fixed charge = Rs 400 and charge per day = Rs 30
