A : B = 3 : 4 and B : C = 5 : 6 Find the C : A

Options

A. `5:2`
B. `15:24`
C. `8:5`
D. `5:8`

Answer

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

### Step 1: Write down the given ratios
We are given:
- A : B = 3 : 4
- B : C = 5 : 6

### Step 2: Express A and C in terms of B
From the ratio A : B = 3 : 4, we can express A in terms of B:
- A = (3/4)B

From the ratio B : C = 5 : 6, we can express C in terms of B:
- C = (6/5)B

### Step 3: Substitute B in terms of A and C
Now, we need to find a common value for B to relate A and C. We can express B in terms of A using the first ratio:
- B = (4/3)A

### Step 4: Substitute B into the expression for C
Now, we substitute B into the equation for C:
- C = (6/5)B = (6/5) * (4/3)A

### Step 5: Simplify the expression for C
Now, simplify the expression for C:
- C = (6 * 4) / (5 * 3) A = 24/15 A

### Step 6: Write the ratio C : A
Now we can write the ratio C : A:
- C : A = (24/15)A : A = 24 : 15

### Step 7: Simplify the ratio
To simplify the ratio 24 : 15, we can divide both numbers by their greatest common divisor, which is 3:
- C : A = 24/3 : 15/3 = 8 : 5

### Final Answer
Thus, the ratio C : A is 8 : 5.

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