If 4/6 of A = 75% of B = 60% of C, then A:B:C is equal to:

Options

A. a. 9:8:10
B. b. 8:9:10
C. c. 3:4:5
D. d. None of these

Answer

To solve the problem, we need to find the ratio A:B:C given that \( \frac{4}{6}A = 75\%B = 60\%C \).

### Step-by-Step Solution:

1. **Convert percentages to fractions**:
- \( 75\% \) can be written as \( \frac{75}{100} = \frac{3}{4} \).
- \( 60\% \) can be written as \( \frac{60}{100} = \frac{3}{5} \).

So, we can rewrite the equation as:
\[ \frac{4}{6}A = \frac{3}{4}B = \frac{3}{5}C \]

2. **Set a common variable**:
Let \( k \) be the common value such that:
\[ \frac{4}{6}A = k, \quad \frac{3}{4}B = k, \quad \frac{3}{5}C = k \]

3. **Express A, B, and C in terms of k**:
- From \( \frac{4}{6}A = k \):
\[ A = k \cdot \frac{6}{4} = \frac{3}{2}k \]
- From \( \frac{3}{4}B = k \):
\[ B = k \cdot \frac{4}{3} = \frac{4}{3}k \]
- From \( \frac{3}{5}C = k \):
\[ C = k \cdot \frac{5}{3} = \frac{5}{3}k \]

4. **Write the ratio A:B:C**:
Now we can express the ratio A:B:C as:
\[ A : B : C = \frac{3}{2}k : \frac{4}{3}k : \frac{5}{3}k \]

5. **Eliminate k**:
Since k is common in all terms, we can ignore it and focus on the coefficients:
\[ A : B : C = \frac{3}{2} : \frac{4}{3} : \frac{5}{3} \]

6. **Find a common denominator**:
The least common multiple of the denominators (2, 3) is 6. So we convert each term:
- \( \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \)
- \( \frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6} \)
- \( \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \)

Thus, we have:
\[ A : B : C = 9 : 8 : 10 \]

### Final Ratio:
The ratio \( A : B : C \) is \( 9 : 8 : 10 \).

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