The ratio of two numbers A and is 5 : 8. If 5 is added to each of A and B, then the ratio of A and B becomes 2 : 3. The sum of A and B is:

65

              A  :  B 

Original   5  :  8           

New        2  :  3

          __________

            +5      +5

⇒ $\frac{5R+5}{8R+5} = \frac{2}{3}$

Using cross - multiplication method, 

16r - 15r = (5 x 3) -(5 x 2)

⇒         r =  5

Sum of A and B = 13r = 65