If $$ \frac{2}{3} $$ of $$ A = 75\% $$ of $$ B = 0.6 $$ of $$ C $$, then the ratio $$ A : C : B $$ is:

Question

Accepted Answer

### Step-by-Step Solution:

1. **Given Relationships:**  
   - $$ \frac{2}{3} A = \frac{75}{100} B = \frac{6}{10} C. $$  
   Simplify each fraction:  
   - $$ \frac{75}{100} = \frac{3}{4}, \quad \frac{6}{10} = \frac{3}{5}. $$  
   Thus, the equation becomes:  
   $$ \frac{2}{3} A = \frac{3}{4} B = \frac{3}{5} C. $$

2. **Express in terms of a common multiplier:**  
   Let $$ A = x, B = y, C = z $$. Using the given relationships:  
   - From $$ \frac{2}{3} A = \frac{3}{4} B $$:  
     $$
     \frac{x}{y} = \frac{\frac{3}{4}}{\frac{2}{3}} = \frac{3 	imes 3}{4 	imes 2} = \frac{9}{8}.
     $$
     Thus, $$ x : y = 9 : 8. $$

- From $$ \frac{3}{4} B = \frac{3}{5} C $$:  
     $$
     \frac{y}{z} = \frac{\frac{3}{5}}{\frac{3}{4}} = \frac{3 	imes 4}{5 	imes 3} = \frac{4}{5}.
     $$
     Thus, $$ y : z = 8 : 10. $$

3. **Combine the ratios:**  
   From the two ratios:  
   - $$ x : y = 9 : 8, y : z = 8 : 10. $$  
   Combine them to get:  
   $$
   x : y : z = 9 : 8 : 10.
   $$

### Final Answer:  
The ratio $$ A : C : B $$ is **9 : 10 : 8**, corresponding to option **(b)**.

Answer

Answer

Answer