Seven years ago, the ratio of the ages of Ajith and Ganesh was 5 : 7. If the product of their present ages is 616, find the ratio of their present age.

Correct option is B

Seven years ago, the ratio of the ages of Ajith and Ganesh was 5 : 7.
Let their ages be measure in terms of x, then their present ages are 5x + 7 and 7x + 7 respectively.
If the product of their present ages is 616,
Then (5x+7) (7x+7) = 616
35x$$^2$$​ + 35 x + 49x + 49 = 616
35x$$^2$$ + 84x + 49-616 = 0 ​
35x$$^2$$ +84x-567 = 0 ​
=>7(5x$$^2$$ + 12x-81) = 0 ​
→5x$$^2$$ + 12x81 = 0 ​
= 5x$$^2$$ + (27 – 15)x – 81 = 0 ​
5x$$^2$$+ 27x-15x - 81 = 0 ​
= x (5x + 27) – 3(5x + 27) = 0
= (5x + 27) (x – 3) = 0
=>x=-27/5 or, x = 3

putting the value of x in 5x + 7 and 7x + 7

                                    =22:28

                                      =11:14

ratio of their present age = 11:14