A certain sum becomes 5 times of itself in 8 years at a rate of simple interest. In 24 years it will become how many times of itself at the same rate of simple interest?

Correct option is B

Given:
Time = 8 years
Sum becomes 5 times itself in 8 years.
Concept Used:
In simple interest, if a sum becomes X times itself in a given time, then interest = (X 1) \times Principal.
Formula Used:
Simple Interest formula: I = $$\frac {P \times R \times T }{ 100}$$​​
(Where P = Principal, R = Rate, T = Time, and I = Simple Interest)
Solution:
Let the principal be X. Since it becomes 5X in 8 years, the interest in 8 years is 4X
​$$4X = \frac{X \times 8 \times R}{100}\\R = \frac{4 \times 100} 8 = 50\%$$​​
Now, for 24 years, the total interest (I) will be:
I = $$X \times R \times \frac{T }{ 100} = X \times 50 \times \frac{24 }{ 100}$$​ = 12X

Therefore, the sum will become: Principal + Interest = X + 12X = 13X
Thus, in 24 years, the sum will become 13 times of itself.