Question

If $\frac{a}{b}=\frac{2}{3}$ and $\frac{b}{c}=\frac{4}{5}$ then find value of $\frac{a+b}{b+c}$.

Answer 1

$\frac{a}{b}=\frac{2}{3}\times \frac{4}{4}=\frac{8}{12}$

$\frac{b}{c}=\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}$

$\therefore a:b:c=8:12:15$

$a=8k,b=12k,c=15k$ ($k=$ constant of proportionality)

$\therefore \frac{a+b}{b+c}=\frac{8k+12k}{12k+15k}=\frac{20k}{27k}=\frac{20}{27}$