IfA : B= 3: 4 andB: C = 8: 9, then find the value ofA : B : C.

Options

A. `5//4`
B. `6 //5`
C. `25 //31`
D. `31 // 42`

Answer

To find the value of A : B : C given the ratios A : B = 3 : 4 and B : C = 8 : 9, we can follow these steps:

### Step 1: Write down the given ratios.
We have:
- A : B = 3 : 4
- B : C = 8 : 9

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

From the second ratio, we can express C in terms of B:
- C = (9/8)B

### Step 3: Find a common term for B.
To combine these ratios, we need to express A, B, and C in terms of a common variable. Let's denote B as a common variable, say B = 32 (which is a common multiple of 4 and 8).

### Step 4: Calculate A and C using B = 32.
Using B = 32:
- A = (3/4) * 32 = 24
- C = (9/8) * 32 = 36

### Step 5: Write the final ratio A : B : C.
Now we can write:
- A : B : C = 24 : 32 : 36

### Step 6: Simplify the ratio.
To simplify the ratio, we can divide each term by the greatest common divisor (GCD) of 24, 32, and 36. The GCD is 4.
- A : B : C = 24/4 : 32/4 : 36/4 = 6 : 8 : 9

Thus, the final answer is:
**A : B : C = 6 : 8 : 9**

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