The ratio of ages of two friends P and Q, four years ago, was 4 : 5. Eight year hence, the ratio of the ages of P and Q will be 11 : 13 . What is the ratio of their present ages ?

9 : 11

4 years ago , ratio of A and B 

               A   :    B

               4   :    5

present age of A = 4x + 4 , present age of B = 5x + 4 

according to question , after 8 years

               A     :    B

               11   :    13

i.e. \(\frac{4x\;+\;12}{5x\;+\;12}\)  =   \(\frac{11}{13}\)

 52x + 156 = 55x + 132

 3x = 24

 x = 8 

present age of A = 4x + 4

so,  P's age ( present ) = 32 + 4 = 36

Q's age  ( present ) = 40 + 4 =44

                     P   : Q 

       Ratio →  36  :  44

                    9    :  11