A party for a group of 50 people was organized on their own expenses. 48 of them paid Rs. 950 each, while the other two paid Rs. 1200 more than the average expenditure of the group. The total expenses incurred was :

Options

A. A. Rs. 75,000
B. B. Rs. 25,000
C. C. Rs. 50,000
D. D. Rs. 40,000

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the total amount paid by the first 48 people.
The first 48 people each paid Rs. 950. Therefore, the total amount paid by these 48 people is:
\[ \text{Total from 48 people} = 48 \times 950 \]

### Step 2: Calculate the total amount paid by the other 2 people.
Let the average expenditure of the group be \( A \). According to the problem, the other two people paid Rs. 1200 more than the average expenditure. Therefore, the amount paid by each of these two people is:
\[ \text{Amount paid by each of the 2 people} = A + 1200 \]
Thus, the total amount paid by the two people is:
\[ \text{Total from 2 people} = 2 \times (A + 1200) \]

### Step 3: Set up the equation for total expenses.
The total expenses incurred by the group can be expressed as:
\[ \text{Total Expenses} = \text{Total from 48 people} + \text{Total from 2 people} \]
Substituting the values from Steps 1 and 2:
\[ \text{Total Expenses} = (48 \times 950) + 2 \times (A + 1200) \]

### Step 4: Calculate the average expenditure \( A \).
The average expenditure \( A \) can also be expressed in terms of total expenses divided by the number of people (50):
\[ A = \frac{\text{Total Expenses}}{50} \]

### Step 5: Substitute \( A \) back into the total expenses equation.
Now we have two equations:
1. Total Expenses = \( (48 \times 950) + 2 \times (A + 1200) \)
2. \( A = \frac{\text{Total Expenses}}{50} \)

We can substitute the expression for \( A \) into the total expenses equation and solve for the total expenses.

### Step 6: Solve for total expenses.
Let's calculate the total from the first 48 people:
\[ 48 \times 950 = 45600 \]
Now substituting \( A \) into the total expenses equation:
\[ \text{Total Expenses} = 45600 + 2 \times \left(\frac{\text{Total Expenses}}{50} + 1200\right) \]
Let \( T \) be the total expenses:
\[ T = 45600 + 2 \times \left(\frac{T}{50} + 1200\right) \]
Expanding this:
\[ T = 45600 + \frac{2T}{50} + 2400 \]
\[ T = 48000 + \frac{2T}{50} \]
Multiplying through by 50 to eliminate the fraction:
\[ 50T = 240000 + 2T \]
Rearranging gives:
\[ 50T - 2T = 240000 \]
\[ 48T = 240000 \]
Dividing both sides by 48:
\[ T = \frac{240000}{48} = 5000 \]

### Final Answer
The total expenses incurred was Rs. 50000.