A hotel incurs 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 Rs. 6000. Also when there are 25 guests average expenses per guests are Rs. 360 ? What is the total expenses of hotel when there are 40 guests?

Options

A. Rs. 8000
B. Rs. 12000
C. Rs. 15500
D. None of these

Answer

To solve the problem step by step, we need to determine the fixed and variable expenses of the hotel based on the information provided.

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

### Step 2: Set up the equations based on the given data
From the problem, we have two scenarios:

1. When there are 10 guests, the total expenses are Rs. 6000:
\[ x + 10y = 6000 \quad \text{(Equation 1)} \]

2. When there are 25 guests, the average expenses per guest are Rs. 360:
\[ \text{Total expenses} = 25 \times 360 = 9000 \]
Therefore, we can write:
\[ x + 25y = 9000 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations
Now we have two equations:
1. \( x + 10y = 6000 \)
2. \( x + 25y = 9000 \)

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

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

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

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

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