With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 3 : 4 . After 4 years, with the same rate of interest, the ratio of the principal and amount becomes  7 : 8 . The rate of interest is?

\(\frac{100}{21}\)%

             P  :   A                     ⇒       P   :  A

              3 : 4     after 4 years          7  :  8 

Since P remains same

               21  : 28                            21 : 24

28 - 24 = 4 ( in 4 years)

SI in 1 year = \(\frac{4}{4}\) = 1

Rate = \(\frac{1}{21}\) × 100 % = \(\frac{100}{21}\)%