If A:B = 5:7, B:C = 6: 11 then A:B :C is

Options

A. `55:77:66`
B. `30:42: 77`
C. `35:49:42`
D. 55:42:96

Answer

To solve the problem of finding the ratio A:B:C given the ratios A:B = 5:7 and B:C = 6:11, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the given ratios**:
- A:B = 5:7
- B:C = 6:11

2. **Identify the common term**:
- The common term in both ratios is B.

3. **Make the B values equal**:
- In the first ratio (A:B), B is 7.
- In the second ratio (B:C), B is 6.
- To make both B values equal, we need to find a common multiple of 7 and 6. The least common multiple (LCM) of 7 and 6 is 42.

4. **Adjust the ratios to have B = 42**:
- For A:B = 5:7, we need to multiply both parts of the ratio by 6 (since 7 * 6 = 42):
- A = 5 * 6 = 30
- B = 7 * 6 = 42
- For B:C = 6:11, we need to multiply both parts of the ratio by 7 (since 6 * 7 = 42):
- B = 6 * 7 = 42
- C = 11 * 7 = 77

5. **Combine the ratios**:
- Now we have:
- A = 30
- B = 42
- C = 77
- Therefore, the combined ratio A:B:C is 30:42:77.

### Final Answer:
A:B:C = 30:42:77

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