If 5.5 of a = 0.65 of b, then a : b is equal to

Options

A. `110:13`
B. `13:11`
C. `11:13`
D. `13:110`

Answer

To solve the problem where \( 5.5 \) of \( a \) equals \( 0.65 \) of \( b \), we need to express this relationship mathematically and find the ratio \( a : b \).

### Step-by-Step Solution:

1. **Set up the equation**:
Given that \( 5.5a = 0.65b \).

2. **Convert the decimals to fractions**:
- \( 5.5 \) can be expressed as \( \frac{55}{10} \).
- \( 0.65 \) can be expressed as \( \frac{65}{100} \).

So, we can rewrite the equation as:
\[ \frac{55}{10}a = \frac{65}{100}b \]

3. **Eliminate the fractions**:
To eliminate the fractions, we can multiply both sides by \( 1000 \) (the least common multiple of the denominators 10 and 100):
\[ 1000 \cdot \frac{55}{10}a = 1000 \cdot \frac{65}{100}b \]
This simplifies to:
\[ 5500a = 650b \]

4. **Rearrange the equation**:
To find the ratio \( a : b \), we can rearrange the equation:
\[ \frac{a}{b} = \frac{650}{5500} \]

5. **Simplify the ratio**:
We can simplify \( \frac{650}{5500} \) by dividing both the numerator and the denominator by \( 50 \):
\[ \frac{650 \div 50}{5500 \div 50} = \frac{13}{110} \]

6. **Express the ratio**:
Therefore, the ratio \( a : b \) is:
\[ a : b = 13 : 110 \]

### Final Answer:
The ratio \( a : b \) is \( 13 : 110 \).

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