Q20 / 50 · Manipal (MET) 2024 · Mathematics
$\frac{a}{b}=\frac{1}{3}$ and $\frac{b}{c}=\frac{3}{4}$, then the value of $\frac{a+2 b}{b+2 c}$ is
- A$\frac{28}{33}$
- Correct answerB$\frac{7}{11}$
- C$\frac{1}{2}$
- DNone of these
Solution
$\because \frac{a}{b}=\frac{1}{3} \Rightarrow b=3 a$ and $\frac{b}{c}=\frac{3}{4} \Rightarrow \frac{3 a}{c}=\frac{3}{4}$
$\Rightarrow \frac{a}{c}=\frac{1}{4} \Rightarrow c=4 a$
Then, $\frac{a+2 b}{b+2 c}=\frac{a+2(3 a)}{(3 a)+2(4 a)}$
$=\frac{a+6 a}{3 a+8 a}=\frac{7 a}{11 a}=\frac{7}{11}$
Hence, the correct answer is option: 'B'.