A hotel incures two types of expenses, one which is fixed and others depend upon no. of guests. When there are 10 guests, total expenses of hotel are ₹ 6000. Also when there are 25 guests average expenses per guests are ₹ 360? What is the total expnses of hotel when there are 40 guests?

Options

A. 8000
B. 12000
C. 15500
D. none of these

Answer

To solve the problem step by step, we will break down the expenses into fixed and variable components.

### Step 1: Define the variables
Let:
- \( F \) = Fixed expenses of the hotel
- \( V \) = Variable expense per guest

### Step 2: Set up the equations based on the given data
1. When there are 10 guests, the total expenses are ₹6000:
\[ F + 10V = 6000 \quad \text{(Equation 1)} \]

2. When there are 25 guests, the average expenses per guest are ₹360. Therefore, the total expenses when there are 25 guests can be calculated as:
\[ \text{Total Expenses} = 25 \times 360 = 9000 \]
Thus, we have:
\[ F + 25V = 9000 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations
Now we have a system of two equations:
1. \( F + 10V = 6000 \)
2. \( F + 25V = 9000 \)

We can subtract Equation 1 from Equation 2 to eliminate \( F \):
\[ (F + 25V) - (F + 10V) = 9000 - 6000 \]
This simplifies to:
\[ 15V = 3000 \]
Now, divide both sides by 15:
\[ V = 200 \]

### Step 4: Substitute \( V \) back to find \( F \)
Now that we have \( V \), we can substitute it back into Equation 1 to find \( F \):
\[ F + 10(200) = 6000 \]
This simplifies to:
\[ F + 2000 = 6000 \]
Subtract 2000 from both sides:
\[ F = 4000 \]

### Step 5: Calculate total expenses for 40 guests
Now we can find the total expenses when there are 40 guests:
\[ \text{Total Expenses} = F + 40V \]
Substituting the values of \( F \) and \( V \):
\[ \text{Total Expenses} = 4000 + 40(200) \]
Calculating \( 40(200) \):
\[ 40(200) = 8000 \]
So,
\[ \text{Total Expenses} = 4000 + 8000 = 12000 \]

### Final Answer
The total expenses of the hotel when there are 40 guests is **₹12000**.

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