The ratio of age of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?

Explanation:-

Ratio of ages of Boys A and B $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{A}}:{\text{B}} \cr & {\text{Present age }}5x:6x \cr & \therefore {\text{After two years }} \cr & \therefore \frac{{5x + 2}}{{6x + 2}} = \frac{7}{8} \cr & \Rightarrow 40x + 16 = 42x + 14 \cr & \Rightarrow 2x = 2 \cr & \Rightarrow x = 1 \cr & \therefore {\text{Present age }} \cr & {\text{A}} = 5 \times 1 = 5 \cr & {\text{B}} = 6 \times 1 = 6 \cr & {\text{After 12 years}} \cr & {\text{A}} = 5 + 12 = 17 \cr & {\text{B}} = 6 + 12 = 18 \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{{17}}{{18}} \cr}$$