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 took food for 27 days she had to pay Rs 1210 as hostel charges whereas a student B, who took food for 15 days, paid Rs 850 as hostel charges. Find the fixed charges and the cost of food per day. [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let the fixed charge be Rs $x$ and Rs $y$ be the cost of food per day.

According to the given condition,

$x+27y=1210\dots \dots \left(i\right)$

$x+15y=850\dots \dots \left(ii\right)$

Equation (i) - (ii) gives,

$x+27y-x-15y=1210-850$

$12y=360$

$\Rightarrow y=30$

Substituting value of y in (i)

$x+27y=1210$

$x+27\left(30\right)=1210$

$\Rightarrow x=400$

$\Rightarrow y=30andx=400$

$\therefore$ The fixed charge is Rs 400 and the cost of food per day is Rs 30.