If 30 % of A = 20 % of B, then find the value of A : B

Options

A. `1 :3`
B. `3 :2`
C. `3 : 1`
D. `2 :3`

Answer

To solve the problem, we need to find the ratio of A to B given that 30% of A is equal to 20% of B.

### Step-by-step Solution:

1. **Write the equation based on the given information**:
\[ 30\% \text{ of } A = 20\% \text{ of } B \]
This can be expressed mathematically as:
\[ \frac{30}{100} \times A = \frac{20}{100} \times B \]

2. **Simplify the percentages**:
We can simplify the fractions:
\[ \frac{3}{10} \times A = \frac{1}{5} \times B \]

3. **Rearrange the equation to find the ratio**:
To find the ratio \( \frac{A}{B} \), we can rearrange the equation:
\[ A = \frac{1}{5} \times B \times \frac{10}{3} \]
This simplifies to:
\[ A = \frac{10}{15} \times B = \frac{2}{3} \times B \]

4. **Express the ratio A:B**:
From the equation \( A = \frac{2}{3} \times B \), we can express the ratio \( A:B \):
\[ \frac{A}{B} = \frac{2}{3} \]
Therefore, the ratio \( A:B \) can be written as:
\[ A:B = 2:3 \]

### Final Answer:
\[ A:B = 2:3 \]