If 15% of A = 20% of B, then `A : B` = ?

Options

A. `3 : 4`
B. `4 : 3`
C. `17 : 16`
D. `16 : 17`

Answer

To solve the problem where 15% of A equals 20% of B, and we need to find the ratio A : B, we can follow these steps:

### Step-by-Step Solution:

1. **Set up the equation based on the given information**:
We know that:
\[ 15\% \text{ of } A = 20\% \text{ of } B \]
This can be expressed mathematically as:
\[ \frac{15}{100} \times A = \frac{20}{100} \times B \]

2. **Eliminate the percentages**:
To simplify the equation, we can multiply both sides by 100 to eliminate the fractions:
\[ 15A = 20B \]

3. **Rearrange the equation to find the ratio**:
We want to express A in terms of B, so we can rearrange the equation:
\[ \frac{A}{B} = \frac{20}{15} \]

4. **Simplify the ratio**:
Now, we can simplify the fraction \(\frac{20}{15}\):
\[ \frac{20}{15} = \frac{4}{3} \]

5. **Write the final ratio**:
Therefore, the ratio of A to B is:
\[ A : B = 4 : 3 \]

### Final Answer:
\[ A : B = 4 : 3 \]