Question

Monthly hostel charges in a college comprises of two parts, one fixed part for the stay in the hostel and the varying part depending on the number of days one has taken food in the mess. Ram takes food for $20$ days and pays Rs. $1700$ as hostel charges and Rahim takes food for $24$ days and pays Rs. $1900$ as hostel charges. Find the fixed charge and the cost of the food per day.

• A. Fixed charge $=$ Rs.$700$ and cost of food per day $=$ Rs. $50$
• B. Fixed charge $=$ Rs. $350$ and cost of food per day $=$ Rs. $20$
• C. Fixed charge $=$ Rs. $500$ and cost of food per day $=$ Rs. $30$
• D. Fixed charge $=$ Rs. $400$ and cost of food per day $=$ Rs. $40$

Answer 1

The correct option is A Fixed charge $=$ Rs.$700$ and cost of food per day $=$ Rs. $50$

Let the food expense per day be $x$ and the constant expense be $y$
Given, $20x+y=1700$ --- $\left(1\right)$
And $24x+y=1900$ -- $\left(2\right)$

Subtracting equation $\left(1\right)$ from $\left(2\right)$, we get

$4x=200\Rightarrow x=50$

Substituting $x=50$ in the equation $\left(1\right)$, we get $20\left(50\right)+y=1700\Rightarrow y=700$

Hence, food expenses per day $=$ Rs. $50$ and fixed charge $=$ Rs. $700$