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 takes food for 20 days she has to pay 1000 as hostel charges whereas a student who takes B food for 26 days, pays 1180 as hostel charges. Find the fixed charges and the cost of food per day.

Answer 1

Let fixed charge for the hostel is `x` rupees and cost for per day food is `y` rupees.
Then,
`x+20y = 1000->(1)`
`x+26y = 1180->(2)`
Subtracting (1) from (2),
`x+26y-x-20y = 1180-1000`
`=>6y = 180`
`=>y = 30`
Putting value of `y` in (1),
`x+20(30) = 1000`
`=>x = 1000-600`
`=>x = 400`
So, fixed charge for the hostel is `400` rupees and cost for per day food is `30` rupees.