If a : b = 2 : 3 and b : c = 4 : 5, then (a + b) : (b + c) is equal to-

Answer: Option C

$$\begin{array}{rl}& \text{a}:\text{b}=\text{2}:\text{3},\\ & \text{b}:\text{c}=\text{4}:\text{5}=\text{4}\times \frac{3}{4}:5\times \frac{3}{4}\\ & =3:\frac{15}{4}\\ & So,a:b:c=2:3:\frac{15}{4}\\ & =8:12:15.\\ & \text{Let}\\ & \text{a}=8\text{k},\\ & \text{b}=12\text{k},\\ & \text{c}=15\text{k}.\\ & \text{Then,}\\ & \frac{\left(\text{a}+\text{b}\right)}{\left(\text{b}+\text{c}\right)}=\frac{\left(8\text{k}+12\text{k}\right)}{\left(12\text{k}+15\text{k}\right)}\\ & =\frac{20\text{k}}{27\text{k}}\\ & =\frac{20}{27}\end{array}$$