A's height is `5//8^(th)` of B's height. What is the ratio of B's height to A's height ?
A. 5:8
B. 3:8
C. 5:3
D. 8:5

Options

A. D
B. A
C. C
D. B

Answer

To solve the problem, we need to find the ratio of B's height to A's height given that A's height is \( \frac{5}{8} \) of B's height.

### Step-by-Step Solution:

1. **Define the Heights**:
Let B's height be represented as \( B \). According to the problem, A's height is \( \frac{5}{8} \) of B's height. Therefore, we can express A's height as:
\[ A = \frac{5}{8} B \]

2. **Set Up the Ratio**:
We need to find the ratio of B's height to A's height, which can be written as:
\[ \text{Ratio} = \frac{B}{A} \]

3. **Substitute A's Height**:
Substitute the expression for A from step 1 into the ratio:
\[ \text{Ratio} = \frac{B}{\frac{5}{8} B} \]

4. **Simplify the Ratio**:
When we simplify the ratio, we can cancel \( B \) from the numerator and the denominator (assuming \( B \neq 0 \)):
\[ \text{Ratio} = \frac{1}{\frac{5}{8}} = \frac{1 \times 8}{5} = \frac{8}{5} \]

5. **Final Ratio**:
Therefore, the ratio of B's height to A's height is:
\[ B : A = 8 : 5 \]

### Conclusion:
The ratio of B's height to A's height is \( 8 : 5 \).