The ratio of the age of X and Y is 6 : 5. Four years ago, that ratio…

             

    X   :    Y      

    5   :    4  ( 4  years ago )         

                 ↓   

    6  :     5  ( present )  

\(\frac{X}{Y}\)  =\(\frac{5}{4}\)

 let age of  X = 5x and age of Y = 4x 

Now , according to question 

\(\frac{5x+4}{4x+4}\) = \(\frac{6}{5}\)

25x  + 20 = 24x + 24 

 x = 4

so,       

X's Present age = 5 x 4 +4 = 24 

Y's Present age= 4 x 4 + 4 = 20

 After 16 years, age of X =16 + 24 = 40

                       age of Y =16 + 20 = 36

             Ratio = 40 : 36

                      = 10 : 9