If A:B = 3:4 and B:C= 6:5 then A:(A+C) is:
A. 9:11
B. 9:10
C. 9:19
D. 6:7

Options

A. D
B. B
C. A
D. C

Answer

To solve the problem, we need to find the ratio A:(A+C) given the ratios A:B and B:C.

### Step-by-Step Solution:

1. **Write down the given ratios**:
- A:B = 3:4
- B:C = 6:5

2. **Express A and B in terms of a common variable**:
- Let A = 3k and B = 4k for some variable k.

3. **Express B and C in terms of a common variable**:
- From B:C = 6:5, we can express B in terms of C:
- Let B = 6m and C = 5m for some variable m.

4. **Equate the two expressions for B**:
- Since B = 4k and B = 6m, we can set them equal to each other:
- 4k = 6m
- This implies k = (6/4)m = (3/2)m.

5. **Substitute k back to find A and C**:
- Substitute k into A:
- A = 3k = 3 * (3/2)m = (9/2)m.
- Substitute m to find C:
- C = 5m.

6. **Calculate A + C**:
- A + C = (9/2)m + 5m = (9/2)m + (10/2)m = (19/2)m.

7. **Find the ratio A:(A+C)**:
- A:(A+C) = (9/2)m : (19/2)m.
- This simplifies to 9:19.

### Final Answer:
The ratio A:(A+C) is 9:19, which corresponds to option C.