Question

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 ₹ 1000 as hostel charges, whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charges and the cost of food per day. Form the pair of linear equations and find these solutions by substitution method.
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Answer 1

Let the fixed charge be Rs. x and the variable charge be Rs. y per day.

It is given that when a student A takes food for 20 days she has to pay Rs. 1000 as hostel charges, therefore,

x+20y=1000

⇒x=1000−20y.....(1)

It is also given that when a student B takes food for 12 days she has to pay Rs. 1180 as hostel charges, therefore, we have:

x+26y=1180

Let us now substitute the value of x from equation 1 as follows:

x+26y=1180

⇒1000−20y+26y=1180

⇒−20y+26y=1180−1000

⇒6y=180

⇒y=

6

180

⇒y=30

Now, substitute the value of y in equation 1:

x=1000−(20×30)=1000−600=400

Therefore, x=400 and y=30.

Hence, the fixed charges is Rs. 400 and the variable charges is Rs. 30 per day.