If A, B, and C are three amounts of money such that B is the simple interest on A, and C is the simple interest on B, all for the same time and at the same rate of interest, then which of the following is true?

Correct option is B

Given:
B is the simple interest on amount A
C is the simple interest on amount B
Rate of interest and time are the same for all
Formula Used:
Simple Interest (SI) = $$\frac {P × R × T}{ 100}$$​​
Solution:
Let the rate of interest be R% per annum and time be T years.
Simple interest on amount A:
B = $$\frac {A × R × T}{ 100}$$​​

Let k = $$\frac {R × T}{ 100}$$​
So, B = A × k
Simple interest on amount B:
C = $$\frac {B × R × T}{ 100}$$​= B × k = A × k²
Now,
B² = (A × k)² = A²k²
A × C = A × (A × k²) = A²k²
Hence,
B² = AC