If with simple interest, an amount doubles in 5 years, how many times of the original amount, will it be after 8 years with same rate of simple interest?

Correct option is C

Given:
An amount doubles in 5 years with simple interest.
The rate of interest remains the same.
Concept Used:
Simple Interest formula:
​$$\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}$$​​
Where:
P = Principal amount
R = Rate of interest
T= Time period
Solution:
Let the principal amount be P.
After 5 years, the amount doubles. So, the total amount after 5 years is 2P.
The simple interest earned in 5 years is:
SI = 2P - P = P
P =$$\frac{P \times R \times 5}{100}$$​

​$$P = \frac{5PR}{100}$$​

​$$R = \frac{100}{5} = 20\%$$​

​$$\text{SI} = \frac{P \times 20 \times 8}{100} = \frac{160P}{100} = 1.6P$$​
​$$\text{Total Amount} = P + \text{SI} = P + 1.6P = 2.6P$$ =2$$\frac{3}{5}P$$​​
After 8 years, the amount will be $$2\frac{3}{5}$$ times the original amount.