The ratio of the number of boys and girls ina college is 6 : 7. Ifthe percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

Options

A. ` 72 : 77 `
B. `35 : 36`
C. `36 : 35 `
D. `77 : 72 `

Answer

To solve the problem, we will follow these steps:

1. **Define the initial quantities of boys and girls**:
Let the number of boys be \(6x\) and the number of girls be \(7x\), where \(x\) is a common multiplier.

2. **Calculate the increase in the number of boys**:
The percentage increase in the number of boys is 20%. Therefore, the new number of boys can be calculated as:
\[ \text{New number of boys} = 6x + (20\% \text{ of } 6x) = 6x + \frac{20}{100} \times 6x = 6x + 1.2x = 7.2x \]

3. **Calculate the increase in the number of girls**:
The percentage increase in the number of girls is 10%. Therefore, the new number of girls can be calculated as:
\[ \text{New number of girls} = 7x + (10\% \text{ of } 7x) = 7x + \frac{10}{100} \times 7x = 7x + 0.7x = 7.7x \]

4. **Determine the new ratio of boys to girls**:
The new ratio of boys to girls is:
\[ \text{New ratio} = \frac{\text{New number of boys}}{\text{New number of girls}} = \frac{7.2x}{7.7x} \]
The \(x\) cancels out:
\[ \text{New ratio} = \frac{7.2}{7.7} \]

5. **Simplify the ratio**:
To simplify \( \frac{7.2}{7.7} \), we can multiply both the numerator and the denominator by 10 to eliminate the decimal:
\[ \frac{7.2 \times 10}{7.7 \times 10} = \frac{72}{77} \]

6. **Final result**:
The new ratio of boys to girls is \(72 : 77\).