If the simple interest for 8 years is equal to 40% of the principal, then after how many years will it be equal to the principal?

Correct option is A

Given:

Simple interest is 40% of the principle

Time = 8 years

Formula Used:

$$SI =\frac{P \times R \times T }{100}$$​​

Solution:

Let the principle be x

Then interest = 40% of x = 0.4x

Hence

​$$0.4x = \frac{x \times R \times 8 }{100}$$​ 

R =5%

If principle and interest are equal then time required:

Principle = Interest =x

Then

​$$x = \frac{ x \times 5 \times t}{100}$$​ 

t = 20years

Alternative Method:

If simple interest is calculated then interest is same each year

Here 40% is accumulated in 8 years

For interest to be 100%

Next 40% will take another 8 years

And remaining 20% will take $$\frac{8}{2}$$​ = 4 years

Total time taken for interest to become equal to principle = 8+8+4 = 20 years