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:

Solution (By Examveda Team)

Formula used:
A = $${\text{P}}\frac{{\left( {1 + {\text{RT}}} \right)}}{{100}}$$
A → Amount
P → Principal
R → Rate
T → Time
Calculation:
A sum at simple interest becomes two times in 8 years
⇒ 2P = $$\frac{{{\text{P}}\left( {1 + {\text{R}} \times {\text{8}}} \right)}}{{100}}$$
⇒ R = $$\frac{{100}}{8}$$
⇒ R = 12.5
∴ The rate of interest is 12.5%
The time in which the same sum will be 4 times
⇒ 4P = $$\frac{{{\text{P}}\left( {1 + 12.5 \times {\text{T}}} \right)}}{{100}}$$
⇒ 300 = 12.5T
⇒ T = 24
∴ The sum will be 4 times in 24 years