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.

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

Then as per the question 

x + 25y = 4500 ………(i) 

x + 30y = 5200 ……..(ii) 

Subtracting (i) from (ii), we get 

5y = 700 

⇒ y = 700/5 = 140 

Now, putting y = 140, we have 

x + 25 × 140 = 4500 

⇒x = 4500 – 3500 = 1000 

Hence, the fixed charges be Rs.1000 and the cost of the food per day is Rs.140.

Let fixed hostel charge (monthly) = Rs x

and cost of food for one day = Rs y

In case of student A,

x + 25y = 1750 …(i)

In case of student B,

x + 28y = 1900 …(ii)

On subtracting Eq. (i) from Eq. (ii), we get

x + 28y – x – 25y = 1900 – 1750

⇒ 3y = 150

⇒ y = 50

On putting the value of y = 50 in Eq. (i), we get

x + 25(50) = 1750

⇒ x + 1250 = 1750

⇒ x = 1750 – 1250 = 500

Hence, monthly fixed charges is Rs. 500 and cost of food per day is Rs. 50