In a class, the number of boys and girls is in the ratio of 4 : 5. If 10 more boys join the class, the ratio of numbers of boys and girls becomes 6 : 5. How many girls are there in the class?

Options

A. 20
B. 30
C. 25
D. Couldn't be determined

Answer

To solve the problem step by step, we will follow the information given in the question and set up equations based on the ratios provided.

### Step 1: Set up the initial ratio
We know that the ratio of boys to girls is 4:5. Let's denote the number of boys as \( x \) and the number of girls as \( y \). According to the ratio, we can write:

\[ \frac{x}{y} = \frac{4}{5} \]

### Step 2: Cross-multiply to form the first equation
Cross-multiplying gives us:

\[ 5x = 4y \quad \text{(1)} \]

### Step 3: Set up the new ratio after boys join
According to the problem, if 10 more boys join the class, the new ratio of boys to girls becomes 6:5. Therefore, we can express this as:

\[ \frac{x + 10}{y} = \frac{6}{5} \]

### Step 4: Cross-multiply to form the second equation
Cross-multiplying this new ratio gives us:

\[ 5(x + 10) = 6y \]

Expanding this, we get:

\[ 5x + 50 = 6y \quad \text{(2)} \]

### Step 5: Solve the system of equations
Now we have two equations:
1. \( 5x - 4y = 0 \) (from equation 1)
2. \( 5x - 6y = -50 \) (from equation 2)

We can subtract equation (1) from equation (2):

\[ (5x - 6y) - (5x - 4y) = -50 - 0 \]

This simplifies to:

\[ -2y = -50 \]

### Step 6: Solve for \( y \)
Dividing both sides by -2 gives:

\[ y = 25 \]

### Step 7: Conclusion
Thus, the number of girls in the class is:

\[ \boxed{25} \]

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