If `A = 1/4B` and `B = 1/2C` , then find the value of A:B:C .

Options

A. `8:4:1`
B. `4: 2: 1`
C. `1 : 4 : 8`
D. `1 : 2 : 4`

Answer

To solve the problem, we need to find the ratio A:B:C given the relationships A = 1/4B and B = 1/2C.

### Step-by-step Solution:

1. **Start with the given equations**:
- A = (1/4)B
- B = (1/2)C

2. **Express B in terms of C**:
- From the second equation, we can express B as:
\[ B = \frac{1}{2}C \]

3. **Substitute B in the equation for A**:
- Now, substitute the expression for B into the equation for A:
\[ A = \frac{1}{4}B = \frac{1}{4} \left(\frac{1}{2}C\right) \]
- Simplifying this gives:
\[ A = \frac{1}{8}C \]

4. **Now we have expressions for A and B in terms of C**:
- A = (1/8)C
- B = (1/2)C
- C = 1C (as it is the base value)

5. **Write the ratios**:
- Now we can express A, B, and C in terms of a common variable (let’s use C):
\[ A : B : C = \frac{1}{8}C : \frac{1}{2}C : C \]

6. **Eliminate C from the ratios**:
- Since C is common in all terms, we can ignore it to simplify the ratio:
\[ A : B : C = \frac{1}{8} : \frac{1}{2} : 1 \]

7. **Convert to a common denominator**:
- To express the ratios in whole numbers, find a common denominator. The common denominator for 8, 2, and 1 is 8:
\[ A : B : C = 1 : 4 : 8 \]

8. **Final Ratio**:
- Therefore, the final ratio A:B:C is:
\[ A : B : C = 1 : 4 : 8 \]

### Final Answer:
A : B : C = 1 : 4 : 8