If
$$ A : B = \frac{1}{2} : \frac{5}{8}, \, B : C = \frac{1}{3} : \frac{4}{5}, \, ext{and} \, C : D = \frac{3}{4} : \frac{5}{16}, $$
then the ratio $$ A : B : C : D $$ is:

Question

If  
$$ A : B = \frac{1}{2} : \frac{5}{8}, \, B : C = \frac{1}{3} : \frac{4}{5}, \, 	ext{and} \, C : D = \frac{3}{4} : \frac{5}{16}, $$  
then the ratio $$ A : B : C : D $$ is:

Accepted Answer

1. **Given Ratios**:  
   - $$ A : B = \frac{1}{2} : \frac{5}{8} $$  
   - $$ B : C = \frac{1}{3} : \frac{4}{5} $$  
   - $$ C : D = \frac{3}{4} : \frac{5}{16} $$

2. **Simplify Each Ratio**:  
   - For $$ A : B $$:  
     $$
     A : B = \frac{\frac{1}{2}}{\frac{5}{8}} = \frac{1}{2} 	imes \frac{8}{5} = \frac{4}{5}.
     $$
   - For $$ B : C $$:  
     $$
     B : C = \frac{\frac{1}{3}}{\frac{4}{5}} = \frac{1}{3} 	imes \frac{5}{4} = \frac{5}{12}.
     $$
   - For $$ C : D $$:  
     $$
     C : D = \frac{\frac{3}{4}}{\frac{5}{16}} = \frac{3}{4} 	imes \frac{16}{5} = \frac{12}{5}.
     $$

3. **Combine Ratios**:  
   To find the combined ratio $$ A : B : C : D $$, multiply the ratios sequentially:  
   - Start with $$ A : B = 4:5 $$.  
   - Combine with $$ B : C = 5:12 $$. The common term is $$ B $$, so:  
     $$
     A : B : C = 4:5:12.
     $$
   - Combine with $$ C : D = 12:5 $$. The common term is $$ C $$, so:  
     $$
     A : B : C : D = 4:5:12:5.
     $$

4. **Final Answer**:  
   The ratio is **4:5:12:5**.

Thus, the correct answer is **C. 4:5:12:5**.

Answer

Answer

Answer