In a school, 10% of number of girls is equal to `1/20`th of number of boys. Ratio between the number of boys to number of girls is

Options

A. `1 : 2`
B. `2 :1`
C. `1 :4`
D. `4:1`

Answer

To solve the problem, we need to find the ratio between the number of boys and the number of girls in a school, given that 10% of the number of girls is equal to 1/20th of the number of boys.

Let's denote:
- The number of boys as \( x \)
- The number of girls as \( y \)

According to the problem, we have the equation:
\[ 10\% \text{ of } y = \frac{1}{20} \text{ of } x \]

Step 1: Convert the percentage into a fraction.
\[ 10\% \text{ of } y = \frac{10}{100} \times y = \frac{1}{10}y \]

Step 2: Rewrite the equation using the fraction.
\[ \frac{1}{10}y = \frac{1}{20}x \]

Step 3: Cross-multiply to eliminate the fractions.
\[ 20 \times \frac{1}{10}y = 1 \times x \]
\[ 2y = x \]

Step 4: Rearrange the equation to find the ratio of boys to girls.
\[ \frac{x}{y} = 2 \]

Step 5: Express the ratio in terms of boys to girls.
\[ \frac{x}{y} = 2 \implies x : y = 2 : 1 \]

Thus, the ratio between the number of boys to the number of girls is \( 2 : 1 \).