Question

A part of monthly hostel charges is fixed and the remaining depends on the days one has

taken food in the mess. When a student A takes food for 20 days. A 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 charge and the cost of food per day.


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Answer 1

Answer:

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Step-by-step explanation:

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=6180

⇒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.

Answer 2

Let the fixed charges = y (in rupees) and the cost of food per day = x (in rupees).

Now, A takes food for 20 days and pays Rs. 1000.

That is, 20x+y=1000 .................(1)

Also, B takes food for 26 days and pays Rs. 1180.

That is, 26x+y=1180 ..................(2)

Subtracting (1) from (2), we get,

6x=180

i.e. x =30

Substitute x=30 in (1), we get,

20(30)+ y=1000

i.e. 600 +y=1000

i.e. y = 400

Hence, the fixed charges are Rs. 400 and the cost of food per day is Rs. 30.