Question

A part of monthly hostel charges in a college is fixed and the remaining depend on the number of days one has taken food in the mess. When a student A, takes food for 22 days, he has to pay Rs. 1380 as hostel charges, whereas a student B, who takes food for 28 days, pays Rs. 1680 as hostel charges. Find the fixed charge and the cost of food per day.

Answer 1

Let fixed hostel charge (monthly) $=\mathrm{Rs}x$ and cost of food for one day = Rs y
In case of student A, $x+22y=1380\dots \left(i\right)$
In case of student B, $x+28y=1680\dots \left(\text{ii}\right)$
On subtracting Eq.(i) from Eq. (ii), we get
$x+28y-x-22y=1680-1380$
$\Rightarrow 6y=300$
$\Rightarrow y=50$
On putting the value of $y=50$ in Eq. (i), we get
$x+22\left(50\right)=1380$
$\Rightarrow x+1100=1380$
$\Rightarrow x=1380-1100=280$
Hence, monthly fixed charges is $Rs.280$ and cost of food per day is $Rs.50$