A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess.

Question

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : 

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.

Answer 1

Fixed hostel charges be Rs. x. 

Amount to be paid be Rs. y. 

x + 20y = 1000 …………. (i) 

x + 26y = 1180 …………. (ii) 

By elimination method we can find solution. 

Subtracting eqn. (ii) from eqn. (i),

∴ y = Rs. 30 

Substituting the value of ‘y’ in eqn. (i), 

x + 20y = 1000 

x + 20(30) = 1000 

x + 600 = 1000 

∴ x = 1000 – 600 

∴ x = Rs. 400 

Fixed charge, x = Rs. 400 

Amount to be paid, y = Rs. 30.