The ratio of age of P and Q is 10 : 13. The ratio of age of P, ten years ago to the age of Q after ten years is 8 : 15. Find ratio of age of P, ten years hence to the age of Q ten years ago.

12 : 11

ratio of →         P      :      Q

                       10    :      13

Let Present age of P = 10x  and  Present age of Q =  13x 

  According to question ,  Ratio of age of P 10 years ago to the age of Q after 10 year is 8 : 15 . 

i.e. ratio of →       P    :     Q

                           8    :    15 

i.e. \(\frac{10x\;-\;10}{13x\;+\;10}\)  =   \(\frac{8}{15}\)

150x - 150 = 104x + 80 

 46x  =  230 

  x = 5

  As, Present age of P = 10x

 P's present age = 10 × 5 = 50

 Q's present age = 13 × 5 = 65

   Ratio of age of P 10 year hence= 50 + 10 =60

    Ratio of age of Q 10 years ago = 65 - 10 =55

required ratio,             P     :    Q               

                                 60    :    55

                                  12   :   11