One year ago , the ratio of age of Amit to Sumit was 3 : 2. The ratio of their respective ages , 13 years from now , will be 4 : 5. What will be ratio of their respective age after 9 years from now ?

8 : 7

                        A      :     S

( 1 Year ago )    3      :     2

Present age of Amit = 3x + 1 , Present age of sumit = 2x + 1 

After 13 years , age of Amit = 3x + 14 , age of Sumit = 2x + 14

Now, \(\frac{3x\; +\; 14}{2x\;+\;14}\) = \(\frac{4}{5}\)

 15x + 70 = 8x + 56

   7x= 14 

    x = 2

Present age of Amit = 3 × 2 + 1 = 7     ,    age of Sumit = 2 × 2 + 1 = 5

                                                    A    :     S

                          After 9 years →   16   :    14

                                                     8   :     7