The ratio of the number of boys and girls of a school with 504 students is `13:11`. What will be the new ratio if 12 more girls are admitted?

Options

A. `91:81`
B. `81:91`
C. `9:10`
D. `10:9`

Answer

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

### Step 1: Understand the given ratio
The ratio of boys to girls is given as 13:11. This means that for every 13 boys, there are 11 girls.

### Step 2: Calculate the total parts in the ratio
To find the total parts represented in the ratio, we add the parts for boys and girls:
\[ \text{Total parts} = 13 + 11 = 24 \]

### Step 3: Determine the value of one part
We know the total number of students in the school is 504. To find the value of one part, we divide the total number of students by the total parts:
\[ \text{Value of one part} = \frac{504}{24} = 21 \]

### Step 4: Calculate the number of boys and girls
Now, we can find the actual number of boys and girls by multiplying the number of parts by the value of one part:
- Number of boys (B):
\[ B = 13 \times 21 = 273 \]
- Number of girls (G):
\[ G = 11 \times 21 = 231 \]

### Step 5: Add the new girls
According to the question, 12 more girls are admitted. We will add this to the current number of girls:
\[ \text{New number of girls} = 231 + 12 = 243 \]

### Step 6: Find the new ratio of boys to girls
Now, we can find the new ratio of boys to girls:
\[ \text{New ratio} = \frac{B}{\text{New number of girls}} = \frac{273}{243} \]

### Step 7: Simplify the ratio
To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD). The GCD of 273 and 243 is 9:
\[ \frac{273 \div 9}{243 \div 9} = \frac{30.33}{27} \]
However, we need to express this in whole numbers. We can multiply both parts by 3 to eliminate the decimal:
\[ \text{New ratio} = \frac{30}{27} \text{ or } 30:27 \]

### Step 8: Final simplification
This can be further simplified by dividing both parts by 3:
\[ \text{Final new ratio} = \frac{10}{9} \text{ or } 10:9 \]

### Final Answer
The new ratio of boys to girls after admitting 12 more girls is **10:9**.

---