If a/b = 2/3 and b/c = 4/5 , then the ration a + bb + c equal to?

Answer: Option A

$$\begin{array}{rl}& \frac{a}{b}\text{ = }\frac{2}{3}\text{ and }\frac{b}{c}\text{ = }\frac{4}{5}\left(\text{Given}\right)\\ & or\frac{c}{b}=\frac{5}{4}\\ & \frac{a+b}{b+c}\\ & =\frac{b\left(\frac{a}{b}+1\right)}{b\left(\frac{c}{b}+1\right)}\\ & =\frac{\frac{a}{b}+1}{\frac{c}{b}+1}\\ & =\frac{\left(\frac{2}{3}+1\right)}{\left(\frac{5}{4}+1\right)}\\ & =\frac{\frac{2+3}{3}}{\frac{5+4}{4}}\\ & =\frac{5\times 4}{3\times 9}\\ & =\frac{20}{27}\\ & \therefore \frac{a+b}{b+c}=\frac{20}{27}\\ & \mathbf{Alternate}:\\ & abc\\ & 2_{\times \left(4\right)}{3}_{\times \left(4\right)}\\ & 4_{\times \left(3\right)}{5}_{\times \left(3\right)}\\ & \overline{\underline{81215}}\\ & \therefore \frac{a+b}{b+c}=\frac{8+12}{12+15}\\ & =\frac{20}{27}\end{array}$$