Question

If \( a : b = 2 : 3 \) and \( b : c = 4 : 3 \), then find \( a : b : c \):

• A. 8 : 12 : 9
• B. 2 : 3 : 8
• C. 2 : 3 : 9
• D. 2 : 3 : 12

Hint:

When solving problems involving multiple ratios, adjust the ratios to have a common term, then combine them to find the final ratio.

Answer 1

The Correct Option is A

We are given two ratios: \[ a : b = 2 : 3 \quad \text{and} \quad b : c = 4 : 3 \] Step 1: To find \( a : b : c \), we first need to express the common term \( b \) in both ratios. We have \( b = 3 \) in the first ratio and \( b = 4 \) in the second. To make the \( b \)'s equal, we multiply the first ratio by 4 and the second ratio by 3: \[ a : b = 2 \times 4 : 3 \times 4 = 8 : 12 \] \[ b : c = 4 \times 3 : 3 \times 3 = 12 : 9 \] Step 2: Now, we can combine the two ratios: \[ a : b : c = 8 : 12 : 9 \] Thus, the ratio is \( 8 : 12 : 9 \).