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 food for 20 days, he has to pay Rs. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charged and the cost of food per day.
Given:
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 food for 20 days, he has to pay Rs. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges.
To do:
We have to find the fixed charged and the cost of food per day.
Solution: Let the fixed charge and the daily charge for mess be $x$ and $y$ respectively.
When a student A takes food for 20 days, he has to pay Rs. 1000 as hostel charges.
This implies,
$x + 20y = 1000$.....(i)
When a student B takes food for 26 days, he has to pay Rs. 1180 as hostel charges.
This implies,
$x + 26y = 1180$.....(ii)
Subtracting equation (i) from equation (ii), we get,
$(x+26y)-(x+20y)=1180-1000$
$x-x+26y-20y=180$
$6y=180$
$y=\frac{180}{6}$
$y=30$
Substituting $y=30$ in equation (i), we get,
$x+20(30)=1000$
$x+600=1000$
$x=1000-600$
$x=400$
The fixed charge is Rs. 400 and the cost of food per day is Rs. 30.
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