If 5.4 of a = 9.9 of b, then what is a : b?

Options

A. `6:7`
B. `11:6`
C. `9:11`
D. `11:13`

Answer

To solve the problem, we need to find the ratio \( a : b \) given that \( 5.4a = 9.9b \).

### Step-by-Step Solution:

1. **Start with the given equation**:
\[ 5.4a = 9.9b \]

2. **Rearrange the equation to isolate \( \frac{a}{b} \)**:
\[ \frac{a}{b} = \frac{9.9}{5.4} \]

3. **Simplify the fraction \( \frac{9.9}{5.4} \)**:
- To eliminate the decimals, multiply both the numerator and the denominator by 10:
\[ \frac{9.9 \times 10}{5.4 \times 10} = \frac{99}{54} \]

4. **Further simplify \( \frac{99}{54} \)**:
- Find the greatest common divisor (GCD) of 99 and 54. The GCD is 9.
- Divide both the numerator and the denominator by 9:
\[ \frac{99 \div 9}{54 \div 9} = \frac{11}{6} \]

5. **Express the ratio \( a : b \)**:
- The ratio \( a : b \) can be written as:
\[ a : b = 11 : 6 \]

### Final Answer:
Thus, the ratio \( a : b \) is \( 11 : 6 \).