Let '$$p$$' be the principal amount and '$$r$$' be the interest rate per annum.

Simple Interest for t years = $$ptr$$

Compound Interest for t years = $$p\left(1+r\right)^t-p$$

From the given information,

$$\frac{\left(p\left(1+r\right)^4-p\right)-4pr}{\left(p\left(1+r\right)^3-p\right)-3pr}=\frac{20}{8}$$

$$\frac{\left(\left(1+r\right)^4-1\right)-4r}{\left(\left(1+r\right)^3-1\right)-3r}=\frac{5}{2}$$

$$2\times\ \left(\left(1+r\right)^4-1-4r\right)=5\times\ \left(\left(1+r\right)^3-1-3r\right)$$

$$2\times\ \left(1+r\right)^4-2-8r=5\times\ \left(1+r\right)^3-5-15r$$

$$2\times\ \left(1+r\right)^4=5\times\ \left(1+r\right)^3-3-7r$$

$$\ 2r^4+8r^3+12r^2+8r+2=\ 5r^3+15r^2+15r+5-3-7r$$

$$\ 2r^4+8r^3+12r^2=\ 5r^3+15r^2$$

$$\ 2r^2+3r-3=0$$

Hence, $$r=\frac{-3\pm\ \sqrt{\ 9+24}}{2\times\ 2}$$

$$r=\frac{-3\pm\ \sqrt{\ 33}}{4}$$

As interest rate cannot be negative,

$$r=\frac{-3+\ \sqrt{\ 33}}{4}$$ 

$$r=0.6861$$

Hence, the approximate value of $$r=69\%$$

Option (A) is correct.