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

Solution (By Examveda Team)

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