A sum of money becomes 6 times at simple interest in 15 years. What is the rate of interest?

Correct option is A

Given:
Sum of money becomes 6 times of itself in 15 years
Formula Used:
​$$\text{Simple Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}$$​​
Amount  = Simple Interest + Principal
Solution:
Let the principal be P.
For 15 years,
​$$\text{SI} = \frac{P \times R \times 15}{100} \\\ \\\Rightarrow \text{SI} = \frac{15PR}{100}\\\ \\\text{A} = \text{SI} + P\\\ \\\Rightarrow 6P = \frac{15PR}{100} + P \\\ \\\Rightarrow 5P = \frac{15PR}{100}\\\ \\\Rightarrow R = \frac{500}{15}\\\ \\\Rightarrow R = \frac{100}{3} \approx 33.33\% \\\ \\\therefore \text{The rate of interest is } 33.33\%.$$​​
Alternate Solution:
Let Principal be P
So, Amount = 6P
And, Interest = 6P – P=  5P
​$$\frac{P \times R \times 15}{100} = 5P \\\ \\\Rightarrow \frac{3R}{100} = 1 \\\ \\\Rightarrow 3R = 100 \\\ \\\Rightarrow R = \frac{100}{3} = 33.33\%$$​​
∴ The rate of interest is 33.33%.