A part of monthly hostel charges in a college hostel 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 ₹4,500, whereas a
student B who takes food for 30 days, has to pay ₹ 5,200. Find the fixed charges per month and the cost of food
per day.

Let's denote the fixed charges per month as \( F \) and the cost of food per day as \( C \).

### Given:
- Student A: 25 days of food, total charge = ₹4,500
- Student B: 30 days of food, total charge = ₹5,200

### Formulating the Equations:
For student A:
\[
F + 25C = 4500
\]

For student B:
\[
F + 30C = 5200
\]

### Solving the System of Equations:
We can solve these two equations to find \( F \) (fixed charges) and \( C \) (cost of food per day).

**Step 1:** Subtract the first equation from the second:
\[
(F + 30C) - (F + 25C) = 5200 - 4500
\]
\[
5C = 700
\]
\[
C = \frac{700}{5} = 140
\]
So, the cost of food per day is ₹140.

**Step 2:** Substitute \( C = 140 \) into the first equation to find \( F \):
\[
F + 25(140) = 4500
\]
\[
F + 3500 = 4500
\]
\[
F = 4500 - 3500 = 1000
\]
So, the fixed charges per month are ₹1,000.

### Final Answer:
- Fixed charges per month, \( F \) = ₹1,000
- Cost of food per day, \( C \) = ₹140

Would you like any further details or explanations?

Here are 5 related questions for practice:
1. If a student takes food for 20 days, how much would they have to pay?
2. What would be the total charge for a student who does not take any food in the mess?
3. How many days would a student need to take food in the mess for the total charge to be ₹6,000?
4. If the fixed charges increase by ₹500, what would be the new total charge for 25 days of food?
5. What if the cost of food per day increases by ₹20, how would that affect the total charge for 30 days of food?

**Tip:** When dealing with word problems, it's crucial to translate the given information into algebraic equations systematically.

Learn how to calculate the fixed charges per month and the cost of food per day in a college hostel based on given examples. Solve linear equations using simultaneous equations to determine these costs effectively.

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