Two numbers are in the ratio 2 : 3. If 5 is subtracted from the first number and six is added to the second number, then the ratio becomes 5 : 12. What would the ratio become when eight is added to each number?

14 : 19

 2  :  3

 5  :  12

________

-5     +6

$\frac{2R-5}{3R+6} = \frac{5}{12}$

Using cross - multiplication method, 

24R - 15R = (6 x 5) - (-5 x 12)

         9R   = 30 + 60

           R   = 10

Numbers = 20, 30

When 8 is added to these numbers,

New ratio = 28 : 38 = 14 : 19