If `1/2` of `A= 2/5` of ` B = 1/3` of C, then A: B: C is equal to

Options

A. `4 : 5 : 6`
B. `6 : 4 : 5`
C. `5 : 4 : 6`
D. `4 : 6 : 5`

Answer

To solve the problem where \( \frac{1}{2} A = \frac{2}{5} B = \frac{1}{3} C \), we need to find the ratio \( A : B : C \).

### Step-by-step Solution:

1. **Set the common value**: Let \( k \) be the common value such that:
\[ \frac{1}{2} A = \frac{2}{5} B = \frac{1}{3} C = k \]

2. **Express A, B, and C in terms of k**:
- From \( \frac{1}{2} A = k \):
\[ A = 2k \]
- From \( \frac{2}{5} B = k \):
\[ B = \frac{5}{2} k \]
- From \( \frac{1}{3} C = k \):
\[ C = 3k \]

3. **Write the ratio \( A : B : C \)**:
\[ A : B : C = 2k : \frac{5}{2}k : 3k \]

4. **Eliminate k from the ratio**:
Since \( k \) is common in all terms, we can write:
\[ A : B : C = 2 : \frac{5}{2} : 3 \]

5. **Convert to whole numbers**:
To eliminate the fraction, multiply all parts of the ratio by 2:
\[ A : B : C = 2 \times 2 : 2 \times \frac{5}{2} : 2 \times 3 = 4 : 5 : 6 \]

### Final Result:
The ratio \( A : B : C \) is:
\[ \boxed{4 : 5 : 6} \]