rs 69 were divided among 115 students so that each girl gets 50 paise less than a boy. Thus each boy recieved twice the paise as each girl recieved. The no. of girls in the class is:

Options

A. 92
B. 42
C. 33
D. 23

Answer

To solve the problem step by step, we need to analyze the distribution of the total amount of Rs. 69 among 115 students, where each girl receives 50 paise less than each boy, and each boy receives twice the amount that each girl receives.

### Step 1: Define Variables
Let the amount each girl receives be \( G \) (in paise) and the amount each boy receives be \( B \) (in paise). According to the problem:
- \( B = 2G \) (each boy receives twice what each girl receives)
- \( G = B - 50 \) (each girl receives 50 paise less than each boy)

### Step 2: Set Up the Equations
From the equations above, we can substitute \( B \) in the second equation:
1. Substitute \( B \) in \( G \):
\[ G = 2G - 50 \]
Rearranging gives:
\[ 50 = 2G - G \implies G = 50 \text{ paise} \]
2. Now substitute \( G \) back to find \( B \):
\[ B = 2G = 2 \times 50 = 100 \text{ paise} \]

### Step 3: Calculate Total Distribution
Now we know:
- Each girl receives 50 paise.
- Each boy receives 100 paise.

Let \( x \) be the number of girls and \( y \) be the number of boys. We know that:
\[ x + y = 115 \quad \text{(total students)} \]
The total amount distributed can be expressed as:
\[ 50x + 100y = 6900 \quad \text{(total amount in paise)} \]

### Step 4: Solve the System of Equations
We can rewrite the first equation for \( y \):
\[ y = 115 - x \]
Substituting \( y \) in the second equation:
\[ 50x + 100(115 - x) = 6900 \]
Expanding this gives:
\[ 50x + 11500 - 100x = 6900 \]
Combining like terms:
\[ -50x + 11500 = 6900 \]
Rearranging gives:
\[ -50x = 6900 - 11500 \]
\[ -50x = -4600 \]
Dividing by -50:
\[ x = \frac{4600}{50} = 92 \]

### Step 5: Find the Number of Boys
Using the value of \( x \) to find \( y \):
\[ y = 115 - 92 = 23 \]

### Conclusion
Thus, the number of girls in the class is \( \boxed{92} \).