A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs. 2.40 the number of girls is

Options

A. A) 35
B. B) 40
C. C) 45
D. D) 50

Answer

To solve the problem, we need to find out how many girls are there when a total of Rs. 312 is divided among 100 boys and girls, with boys receiving Rs. 3.60 each and girls receiving Rs. 2.40 each.

### Step-by-Step Solution:

1. **Define Variables:**
Let the number of boys be \( b \) and the number of girls be \( g \).
We know that:
\[ b + g = 100 \quad \text{(1)} \]

2. **Set Up the Equation for Total Amount:**
The total amount distributed among boys and girls is Rs. 312. The total amount received by boys and girls can be expressed as:
\[ 3.60b + 2.40g = 312 \quad \text{(2)} \]

3. **Substitute \( b \) from Equation (1) into Equation (2):**
From equation (1), we can express \( b \) in terms of \( g \):
\[ b = 100 - g \]
Now, substitute \( b \) in equation (2):
\[ 3.60(100 - g) + 2.40g = 312 \]

4. **Simplify the Equation:**
Distributing \( 3.60 \):
\[ 360 - 3.60g + 2.40g = 312 \]
Combine like terms:
\[ 360 - 1.20g = 312 \]

5. **Isolate \( g \):**
Subtract 360 from both sides:
\[ -1.20g = 312 - 360 \]
\[ -1.20g = -48 \]
Now, divide both sides by -1.20:
\[ g = \frac{-48}{-1.20} = 40 \]

6. **Find the Number of Boys:**
Substitute \( g \) back into equation (1) to find \( b \):
\[ b + 40 = 100 \]
\[ b = 100 - 40 = 60 \]

### Conclusion:
The number of girls is \( g = 40 \).