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 $26$ days, pays Rs. $1180$ as hostel charges. Find the fixed charges and the cost of food per day.

• A. Fixed charge: Rs. $700$ and Cost of food per day: Rs. $20$
• B. Fixed charge: Rs. $400$ and Cost of food per day: Rs. $30$
• C. Fixed charge: Rs. $200$ and Cost of food per day: Rs. $10$
• D. Fixed charge: Rs. $500$ and Cost of food per day: Rs. $80$

Answer 1

The correct option is B Fixed charge: Rs. $400$ and Cost of food per day: Rs. $30$

Let the food expense per day be Rs. $x$ and the constant expense be Rs. $y$
Given, $20x+y=1000$ --- $\left(1\right)$
And $26x+y=1180$ -- $\left(2\right)$
Subtracting equation $\left(1\right)$ from $\left(2\right)$, we get $6x=180\Rightarrow x=30$
Substituting $x=30$ in the equation $\left(1\right)$, we get $20\left(30\right)+y=1000\Rightarrow y=400$

Hence, food expenses per day $=$ Rs. $30$ and fixed charge $=$ Rs. $400$