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 Rs.1000 as hostel charges whereas a student B, who takes food for 12 days, pays Rs.1180 as hostel charges. Find the fixed charges and the cost of food per day.
A. 200 and 20
B. 400 and 40
C. 300 and 30
D. 400 and 30

Answer 1

Hint: In this particular type of question we need to form two equations taking x as the fixed charge and y as the additional charge per day. Finally we need to solve for x and y to get the desired result.

Complete step-by-step answer:

Let the fixed charge be Rs. x and the variable charge be Rs. y per day.
It is given that student A takes food for 20 days and pays Rs. 1000 as hostel charges, therefore,
x+20y=1000
$ \Rightarrow $x=1000−20y (1)
It is also given that when a student B takes food for 12 days and 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
$ \Rightarrow $1000−20y+26y=1180
$ \Rightarrow $−20y+26y=1180−1000
$ \Rightarrow $6y=180
$ \Rightarrow $y=30
Now, substitute the value of y in equation 1,
$ \Rightarrow $ x = $1000 - \left( {20 \times 30} \right) = 1000 - 600 = 400$
Therefore, x=400 and y=30.
Hence, the fixed charge is Rs. 400 and the variable charge is Rs. 30 per day.

Note: Note that the fixed charge is the minimum charge that has to be given in the hostel. Another method of solving the equations is to subtract both of them to find the value of y and then substituting it to get the value of x.