With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 2 : 3 . After 2 years, with the same rate of interest, the ratio of the principal and amount becomes 4 : 5 . The rate of interest is?

12.5%

             P  :   A                     ⇒       P  :  A

              2 : 3     after 2 years          4 : 5 

Since P remains same

               4  : 6                            4 : 5

6 - 5 = 1 ( in 2 years)

SI in 1 year = \(\frac{1}{2}\) = 0.5

Rate = \(\frac{0.5}{4}\) × 100 % = 12.5%