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. Then the fixed charges for both $A$ and $B$ must be Rs. $400$.

• A. True
• B. False

Answer 1

The correct option is A True

Let $x$ represent the fixed charges and $y$ represent the number of days the student takes food.
Then,
$x+20y=1000......\left(1\right)$
$x+26y=1180......\left(2\right)$
$\left(1\right)-\left(2\right)\Rightarrow -6y=-180\Rightarrow y=30$
Substitute the value of $y$ in $\left(1\right)$
$\Rightarrow x+20\left(30\right)=1000\Rightarrow x=1000-600\Rightarrow x=400$.
Therefore, the fixed charges is Rs. $400$
The correct answer is $A$.