A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess.
A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes foods for 20 days, he has to pay Rs 1000 as hostel charges whereas a students B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.
Let the fixed charges of hostel be $R s . x$ and the cost of food charges be $R s . y$ per day
According to the given condition we have,
$x+20 y=1000 \cdots(i)$
$x+26 y=1180 \cdots(i i)$
Subtracting equation $(i i)$ from equation $(i)$ we get
$y=30$
Putting $y=30$ in equation $(i)$ we get
$x+20 y=1000$
$x+20 \times 30=1000$
$x+600=1000$
$x=1000-600$
$x=400$
Hence, the fixed charges of hostel is Rs 400
The cost of food per day is Rs 30