If 4.8% of a = 1.05% of b, then what is a : b?

Options

A. `9 : 29`
B. `7 : 32`
C. `1 : 3`
D. `25 : 32`

Answer

To solve the problem, we need to find the ratio \( a : b \) given that \( 4.8\% \) of \( a \) is equal to \( 1.05\% \) of \( b \).

### Step-by-step Solution:

1. **Set Up the Equation:**
We start with the equation given in the problem:
\[ 4.8\% \text{ of } a = 1.05\% \text{ of } b \]
This can be expressed mathematically as:
\[ \frac{4.8}{100} \cdot a = \frac{1.05}{100} \cdot b \]

2. **Eliminate the Percentages:**
To simplify, we can multiply both sides by \( 100 \) to eliminate the percentages:
\[ 4.8a = 1.05b \]

3. **Rearranging the Equation:**
We can rearrange this equation to express \( a \) in terms of \( b \):
\[ \frac{a}{b} = \frac{1.05}{4.8} \]

4. **Simplifying the Fraction:**
Now we simplify \( \frac{1.05}{4.8} \). To do this, we can convert both numbers to fractions:
\[ 1.05 = \frac{105}{100} \quad \text{and} \quad 4.8 = \frac{48}{10} \]
Therefore,
\[ \frac{1.05}{4.8} = \frac{\frac{105}{100}}{\frac{48}{10}} = \frac{105 \times 10}{48 \times 100} = \frac{1050}{4800} \]

5. **Further Simplifying:**
We can simplify \( \frac{1050}{4800} \) by dividing both the numerator and the denominator by \( 30 \):
\[ \frac{1050 \div 30}{4800 \div 30} = \frac{35}{160} \]
We can simplify this further by dividing by \( 5 \):
\[ \frac{35 \div 5}{160 \div 5} = \frac{7}{32} \]

6. **Final Ratio:**
Thus, we have:
\[ \frac{a}{b} = \frac{7}{32} \]
Therefore, the ratio \( a : b \) is:
\[ a : b = 7 : 32 \]

### Conclusion:
The final answer is \( 7 : 32 \).