If A : B = 2 : 3 and B : C = 4 : 5, then what is A : B : C?

Options

A. `8 : 12 : 15`
B. `2 : 3 : 5`
C. ` 2 : 4 : 5`
D. `3 : 5 : 2`

Answer

To solve the problem of finding the ratio A : B : C given that A : B = 2 : 3 and B : C = 4 : 5, we can follow these steps:

### Step 1: Write down the given ratios
We have:
- A : B = 2 : 3
- B : C = 4 : 5

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

From the ratio B : C = 4 : 5, we can express C in terms of B:
- C = (5/4)B

### Step 3: Find a common value 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.

Let B = 12 (the least common multiple of the denominators 3 and 4):
- A = (2/3) * 12 = 8
- C = (5/4) * 12 = 15

### Step 4: Write the final ratio
Now we can write the ratio A : B : C:
- A : B : C = 8 : 12 : 15

### Step 5: Simplify the ratio (if necessary)
The ratio 8 : 12 : 15 is already in its simplest form.

Thus, the final answer is:
**A : B : C = 8 : 12 : 15**

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