Four years ago the ratio of age of A and B was 4 : 5. After 8 years that ratio will be 11 : 13. Find the sum of present age of A and B.

80 years

     X   :    Y      

    4    :    5  ( 4  years ago )         

                 ↓   

    11  :     13  ( 8 years ago )  

\(\frac{X}{Y}\)  =\(\frac{4}{5}\)

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

Now , according to question 

\(\frac{4x+12}{5x+12}\) = \(\frac{11}{13}\)

52x  + 156 = 55x + 132 

3x = 24

x = 8

so,            

X's Present age = 4x8 +4 = 36 

Y's Present age= 5x8 + 4 = 44

Sum = 80