Question

If \( \frac{a}{b} = \frac{1}{3} \) and \( \frac{b}{c} = \frac{3}{4} \), then the value of \( \frac{a+2b}{b+2c} \) is:

• A. \( \frac{28}{33} \)
• B. \( \frac{7}{11} \)
• C. \( \frac{1}{2} \)
• D. None of these

Hint:

Convert ratios into variables for quick simplification.

Answer 1

The Correct Option is B

Concept: Convert ratios into actual values.

Step 1: \[ \frac{a}{b} = \frac{1}{3} \Rightarrow a = k, \; b = 3k \]

Step 2: \[ \frac{b}{c} = \frac{3}{4} \Rightarrow b = 3m, \; c = 4m \] Match \(b\): \[ 3k = 3m \Rightarrow k = m \] So: \[ a = k,\; b = 3k,\; c = 4k \]

Step 3: \[ \frac{a+2b}{b+2c} = \frac{k + 2(3k)}{3k + 2(4k)} = \frac{k + 6k}{3k + 8k} \] \[ = \frac{7k}{11k} = \frac{7}{11} \]