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

The correct option is D 400 and 30

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,

$x+20y=1000\Rightarrow x=1000-20y.....\left(1\right)$

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:

$x+26y=1180\Rightarrow 1000-20y+26y=1180\Rightarrow -20y+26y=1180-1000\Rightarrow 6y=180\Rightarrow y=\frac{180}{6}\Rightarrow y=30$

Now, substitute the value of $y$ in equation 1:

$x=1000-(20\times 30)=1000-600=400$

Therefore, $x=400$ and $y=30$.

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