At certain rate of simple interest, the ratio of the sum and the amount for a certain period of time is 4 : 5. After 3 more years, the ratio becomes 5 : 7. The rate of interest is:

5%

                                    Principal     :     Amount

At present ,                       4           :         5   

After 3 years ,                   5           :         7

As principal is same . So,

                                    Principal     :     Amount

At present ,                    (   4           :         5   ) × 5

After 3 years ,                (   5           :         7   ) × 4

At present ,                      20           :         25

After 3 years ,                  20           :         28

So, Simple Interest of 3 years = 3

Simple Interest of 1 year = 1

Rate of interest = (SI / P) × 100%

= (1 / 20) × 100%

= 5%

The correct answer is Option (2) → 5%