Question

(b) A part of the 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 13000 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

Answer:

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= 180/60

⇒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.