The ratio of the age of A and B is 10 : 13. The ratio of the age of A, ten years ago to the age of B after ten year is 08 : 15. Find the ratio of the age of A, ten years hence to the age of B ten year ago.

12 : 11

     A   :    B      

    10   :    13         

    ↓-10    ↓+10   

     8    :     15

\(\frac{A}{B}\)  =\(\frac{10}{13}\)

 let age of  A = 10x and age of B = 13x 

Now , according to question 

\(\frac{10x-10}{13x+10}\) = \(\frac{8}{15}\)

150x  - 150 = 104x + 80 

46x = 230 

x = 5 

so,

A's age 10 hence  = 10x5 + 10 = 60              

B's age 10 years ago = 13x5 - 10 = 55

Ratio = 60 : 55 = 12 : 11