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?
\(B^2 = AC\)
Step 1 – introduce a common factor:
Let \(r = \dfrac{R \times T}{100}\) (rate × time / 100). Then SI on any principal P is \(P \cdot r\).
Step 2 – express B and C:
\(B = A \cdot r\)
\(C = B \cdot r = (A \cdot r) \cdot r = A r^2\)
Step 3 – check which option holds:
\(B^2 = (A r)^2 = A^2 r^2\)
\(A C = A \cdot A r^2 = A^2 r^2\)
So \(B^2 = A C\).
Hence the correct relation is \(B^2 = AC\).
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