The weight of two from balls are 3.5 kg and 7.5 kg. What is the percentage weight of the first ball with respect to second ball ?

Options

A. `46 (2)/(3)%`
B. `35%`
C. `46(1)/(3)%`
D. `45%`

Answer

To find the percentage weight of the first ball with respect to the second ball, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the weights of the balls**:
- Weight of the first ball (W1) = 3.5 kg
- Weight of the second ball (W2) = 7.5 kg

2. **Set up the formula for percentage**:
- The formula to find the percentage of one quantity with respect to another is:
\[ \text{Percentage} = \left( \frac{\text{Weight of first ball}}{\text{Weight of second ball}} \right) \times 100 \]

3. **Substitute the weights into the formula**:
- Substitute W1 and W2 into the formula:
\[ \text{Percentage} = \left( \frac{3.5}{7.5} \right) \times 100 \]

4. **Calculate the fraction**:
- First, calculate \( \frac{3.5}{7.5} \):
\[ \frac{3.5}{7.5} = \frac{35}{75} = \frac{7}{15} \]

5. **Convert the fraction to a percentage**:
- Now, multiply by 100:
\[ \text{Percentage} = \left( \frac{7}{15} \right) \times 100 \]
- Calculate:
\[ \text{Percentage} = \frac{700}{15} \approx 46.67\% \]

6. **Final answer**:
- The percentage weight of the first ball with respect to the second ball is approximately **46.67%**.