Question

A part of monthly hostel charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25 days, he has to pay Rs. 4550 as hostel charges whereas a student B, who takes food for 30 days, pays Rs. 5200 as hostel charges. Find the fixed charges and the cost of the food per day.

Answer 1

Let the fixed charges be Rs. \(x\) and the cost of food per day be Rs.y.
Then as per the question
$$
x+25 y=4500 \ldots \ldots \ldots \text { (i) }
$$
$$
x+30 y=5200 \ldots \ldots \text {..(ii) }
$$
Subtracting (i) from (ii), we get
$$
\begin{aligned}
&5 y=700 \\
&\Rightarrow y=700 / 5=140
\end{aligned}
$$
Now, putting \(y=140\), we have
$$
\begin{aligned}
&x+25 \times 140=4500 \\
&\Rightarrow x=4500-3500=1000
\end{aligned}
$$
Hence, the fixed charges be Rs. 1000 and the cost of the food per day is Rs. 140 .

Answer 2

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