The number of boys is more than the number of girls by 12% of the total strength of the class. The ratio of the number of boys to that of the girls is

Options

A. ` 11 : 14`
B. ` 14 : 11`
C. ` 25 : 28`
D. ` 28 : 25`

Answer

To solve the problem step by step, we will define the variables and use the information given in the question to find the ratio of the number of boys to the number of girls.

### Step-by-Step Solution:

1. **Define Variables:**
Let the number of boys be \( X \) and the number of girls be \( Y \).

2. **Understand the Given Information:**
The problem states that the number of boys is more than the number of girls by 12% of the total strength of the class. The total strength of the class can be represented as \( X + Y \).

3. **Set Up the Equation:**
According to the problem, we can write the equation:
\[ X = Y + 0.12(X + Y) \]
This means the number of boys \( X \) is equal to the number of girls \( Y \) plus 12% of the total number of students.

4. **Simplify the Equation:**
Substitute \( X + Y \) in the equation:
\[ X = Y + 0.12X + 0.12Y \]
Rearranging gives:
\[ X - 0.12X = Y + 0.12Y \]
This simplifies to:
\[ 0.88X = 1.12Y \]

5. **Find the Ratio:**
Now, we want to find the ratio of the number of boys to the number of girls, which is \( \frac{X}{Y} \). From the equation \( 0.88X = 1.12Y \), we can express \( \frac{X}{Y} \) as follows:
\[ \frac{X}{Y} = \frac{1.12}{0.88} \]

6. **Simplify the Ratio:**
To simplify \( \frac{1.12}{0.88} \), we can multiply both the numerator and the denominator by 100 to eliminate the decimals:
\[ \frac{112}{88} \]
Now, divide both the numerator and the denominator by 8:
\[ \frac{112 \div 8}{88 \div 8} = \frac{14}{11} \]

7. **Conclusion:**
The ratio of the number of boys to the number of girls is \( 14:11 \).