A sum at simple interest becomes two times in 8 years at a certain rate of interest p.a. The time in which the same sum will be 4 times at the same rate of interest at simple interest is:

Let the principal amount = P

Rate of interest = R

Time = 8 years

Amount = 2P

$$\Rightarrow$$  2P = Principal amount + Simple Interest

$$\Rightarrow$$  2P = P + $$\frac{\text{P}\times8\times \text{R}}{100}$$

$$\Rightarrow$$  P =  $$\frac{\text{P}\times8\times \text{R}}{100}$$

$$\Rightarrow$$  R = 12.5%

Let the time in which sum will be 4 times at the same rate of interest = T

i.e, Amount = 4P

$$\Rightarrow$$  4P = P + $$\frac{\text{P}\times \text{T}\times12.5}{100}$$

$$\Rightarrow$$  3P = $$\frac{\text{P}\times \text{T}\times12.5}{100}$$

$$\Rightarrow$$  3 = $$\frac{\text{T}}{8}$$

$$\Rightarrow$$  T = 24 years

$$\therefore\ $$The time in which the same sum will be 4 times at the same rate of interest = 24 years

Hence, the correct answer is Option D