Question : if $\frac{a}{b}=\frac{2}{3}$ and $\frac{b}{c}=\frac{4}{5}$, then $(a+b):(b+c)$=?
Option 1: 3 : 4
Option 2: 4 : 5
Option 3: 5 : 9
Option 4: 20 : 27
Correct Answer: 20 : 27
Solution :
Given:
$\frac{a}{b}=\frac{2}{3}$
⇒ $\frac{a}{b}=\frac{8}{12}$-----------(i)
$\frac{b}{c}=\frac{4}{5}$
⇒ $\frac{b}{c}=\frac{12}{15}$-----------(ii)
From (i) and (ii), we get,
⇒ $a:b:c=8:12:15$
Let $a=8k, b =12k$ and $c=15k$
$\therefore (a+b):(b+c)=(8k+12k):(12k+15k)=20k:27k=20:27$
Hence, the correct answer is 20 : 27.
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