If 10 : 13 is the ratio of present age of A and B respectively and 8 : 15 is the ratio between A's age 10 years ago and B's age 10 years hence, then what will be the ratio of A's age 10 years hence and B's age 10 years ago?

12 : 11

 A    :   B

10   :   13  (present age)

ATQ,

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

⇒ 150x - 150 = 104x + 80

⇒ 46x = 230

⇒ x = 5

Now,  A      :      B

        50            65    (present age)

       +10          -10   

        60             55   (age required as per condition)

        12     :      11