A sum of money invested at simple interest triples itself in 8 years and becomes n times in 20 years. What is the value of n?

Correct option is B

Given:

A sum of money triples itself in 8 years.

Let the principal be P and the rate of interest be R.

It becomes n times in 20 years.

Concept Used:

Simple Interest (SI) is given by the formula:

SI = P × R × T / 100

Total Amount (A) = Principal + Simple Interest

Solution:

When the sum triples in 8 years:

=> A = 3P, T = 8 years

Using the formula for Simple Interest:

SI = A - P

=> 3P - P = P × R × 8 / 100

=> 2P = 8P × R / 100

=> R = 25%

Now, to find n when T = 20 years:

Using the formula for Simple Interest:

SI = P × R × 20 / 100

SI = P × 25 × 20 / 100

SI = 5P

Total Amount (A) = Principal + Simple Interest

A = P + 5P = 6P

Thus, the sum becomes 6 times in 20 years.

Hence, the value of n is 6.