In a class, the ratio of boys to girls is 4:5. If four new boys joined the class, the number of boys would increase by 20%. Find the number of girls in the class.

Options

A. 30
B. 35
C. 20
D. 25

Answer

To solve the problem step by step, we will break down the information provided and use algebra to find the number of girls in the class.

### Step 1: Define the variables
Let the number of boys in the class be \( B \) and the number of girls be \( G \). According to the problem, the ratio of boys to girls is given as 4:5.

### Step 2: Set up the ratio
From the ratio \( \frac{B}{G} = \frac{4}{5} \), we can express the number of boys in terms of girls:
\[ B = \frac{4}{5}G \]

### Step 3: Understand the increase in boys
The problem states that if 4 new boys join the class, the number of boys increases by 20%. This means:
\[ B + 4 = B + 0.2B \]
This simplifies to:
\[ B + 4 = 1.2B \]

### Step 4: Rearrange the equation
Now, we can rearrange the equation to find \( B \):
\[ 1.2B - B = 4 \]
\[ 0.2B = 4 \]

### Step 5: Solve for \( B \)
To find \( B \), divide both sides by 0.2:
\[ B = \frac{4}{0.2} = 20 \]

### Step 6: Substitute \( B \) back to find \( G \)
Now that we have \( B = 20 \), we can substitute it back into the equation for \( G \):
\[ 20 = \frac{4}{5}G \]
To find \( G \), multiply both sides by \( \frac{5}{4} \):
\[ G = 20 \times \frac{5}{4} = 25 \]

### Conclusion
The number of girls in the class is \( G = 25 \).