If A/2= B/3=C/5, then what is `A:B:C` ?

Options

A. `2:3:5`
B. `3:2:5`
C. `3:5:2`
D. `5:3:2`

Answer

To solve the problem, we start with the given equation:

1. **Given**: \( \frac{A}{2} = \frac{B}{3} = \frac{C}{5} \)

2. **Let**: Set the common value of \( \frac{A}{2} = \frac{B}{3} = \frac{C}{5} \) to a constant \( K \).

3. **Express A, B, and C in terms of K**:
- From \( \frac{A}{2} = K \), we can express \( A \) as:
\[ A = 2K \]
- From \( \frac{B}{3} = K \), we can express \( B \) as:
\[ B = 3K \]
- From \( \frac{C}{5} = K \), we can express \( C \) as:
\[ C = 5K \]

4. **Now we have**:
- \( A = 2K \)
- \( B = 3K \)
- \( C = 5K \)

5. **Finding the ratio \( A:B:C \)**:
- We can write the ratio as:
\[ A : B : C = 2K : 3K : 5K \]

6. **Since K is a common factor, we can simplify the ratio**:
- Dividing each term by \( K \) gives:
\[ A : B : C = 2 : 3 : 5 \]

7. **Final answer**:
- Therefore, the ratio \( A:B:C \) is \( 2:3:5 \).