In a school there are 650 students. The ratio of the boys to that fo the girls is 8:5. How many more girls should join the school so that the ratio becomes 4:3?

Options

A. 25
B. 50
C. 100
D. 200

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the number of boys and girls in the school.
Given the total number of students is 650 and the ratio of boys to girls is 8:5.

Let the number of boys be \( 8x \) and the number of girls be \( 5x \).

The total number of students can be expressed as:
\[ 8x + 5x = 650 \]
\[ 13x = 650 \]
Now, we solve for \( x \):
\[ x = \frac{650}{13} = 50 \]

Now, we can find the number of boys and girls:
- Number of boys:
\[ 8x = 8 \times 50 = 400 \]
- Number of girls:
\[ 5x = 5 \times 50 = 250 \]

### Step 2: Set up the equation for the new ratio.
We need to find how many more girls (let's call this \( x \)) should join the school so that the new ratio of boys to girls becomes 4:3.

The new number of girls will be \( 250 + x \).

The ratio can be set up as:
\[ \frac{400}{250 + x} = \frac{4}{3} \]

### Step 3: Cross-multiply to solve for \( x \).
Cross-multiplying gives us:
\[ 400 \times 3 = 4 \times (250 + x) \]
\[ 1200 = 1000 + 4x \]

### Step 4: Isolate \( x \).
Now, we isolate \( x \):
\[ 1200 - 1000 = 4x \]
\[ 200 = 4x \]
\[ x = \frac{200}{4} = 50 \]

### Step 5: Conclusion.
Therefore, the number of girls that should join the school is **50**.

---