The ratio of number of boys to the number of girls in a school of 432, pupils is `5 : 4`. When some new boys and girls are admitted, the number of boys increase by 12 and the ratio of the boys to girls changes to `7 : 6`. The number of new girls admitted is:

Options

A. 12
B. 14
C. 24
D. 20

Answer

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

### Step 1: Determine the initial number of boys and girls.
Given the total number of pupils in the school is 432 and the ratio of boys to girls is 5:4, we can express the number of boys and girls in terms of a common variable.

Let the number of boys be \( 5x \) and the number of girls be \( 4x \).

The equation for the total number of pupils is:
\[ 5x + 4x = 432 \]
\[ 9x = 432 \]
\[ x = \frac{432}{9} = 48 \]

Now, we can find the number of boys and girls:
\[ \text{Number of boys} = 5x = 5 \times 48 = 240 \]
\[ \text{Number of girls} = 4x = 4 \times 48 = 192 \]

### Step 2: Determine the new number of boys after admission.
According to the problem, the number of boys increases by 12:
\[ \text{New number of boys} = 240 + 12 = 252 \]

### Step 3: Set up the equation for the new ratio.
The new ratio of boys to girls is given as 7:6. Let the new number of girls be \( y \). Therefore, we can write the ratio as:
\[ \frac{252}{y} = \frac{7}{6} \]

### Step 4: Cross-multiply to find the new number of girls.
Cross-multiplying gives us:
\[ 252 \times 6 = 7 \times y \]
\[ 1512 = 7y \]
\[ y = \frac{1512}{7} = 216 \]

### Step 5: Calculate the number of new girls admitted.
Initially, there were 192 girls. The new number of girls is 216. Thus, the number of new girls admitted is:
\[ \text{New girls admitted} = 216 - 192 = 24 \]

### Final Answer:
The number of new girls admitted is **24**.

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