The ratio of the present age of two girls is 3 : 4. After two year the ratio will be 7 : 9. Which of the following statement(s) is/are correct ?

I. Ratio of their ages after 10 year is 6 : 7.

II. Ratio of their ages after 12 year is 6 : 7.

Only II

                          I  :  II 

Present ages       3  :  4

After 2 years,      7  :  9

_______________________

                        +2     +2

⇒ $\frac{3R+2}{4R+2} = \frac{7}{9}$

Using cross - multiplication method, 
28R - 27R = (9 x 2) - (7 x 2) 

⇒          R = 4

Present ages = 12, 16

Ratio of ages after 10 years = 22 : 26 = 11 : 13

                            12 years = 24 : 28 = 6 : 7

Therefore, only II statement is correct