Question

If \(a : b = 3 : 4\) and \(b : c = 8 : 9\), then \(a : c\) is

• A. 1 : 3
• B. 3 : 2
• C. 1 : 2
• D. 2 : 3

Hint:

When combining ratios, make sure the common terms are equal before combining the ratios.

Answer 1

The Correct Option is C

We are given that: \[ a : b = 3 : 4 \quad \text{and} \quad b : c = 8 : 9 \] To find \(a : c\), we need to make the value of \(b\) in both ratios the same. The least common multiple (LCM) of 4 and 8 is 8. So, we multiply the first ratio by 2: \[ a : b = 6 : 8 \quad \text{and} \quad b : c = 8 : 9 \] Now, we can combine the ratios: \[ a : c = 6 : 9 = 2 : 3 \] Thus, the correct answer is \(a : c = 2 : 3\).