Suppose ₹X is invested, and after 2 years at 5% simple interest, it yields ₹Y interest. If ₹Y is then invested for 2 years at 5% simple interest, it yields ₹Z interest. Which of the following is true?
\(Y^2 = XZ\)
Apply the simple interest formula \(\text{SI} = \dfrac{P \times R \times T}{100}\) in both stages.
Stage 1 – ₹X invested for 2 years at 5%:
\(Y = \dfrac{X \times 5 \times 2}{100} = \dfrac{X}{10}\)
Stage 2 – ₹Y invested for 2 years at 5%:
\(Z = \dfrac{Y \times 5 \times 2}{100} = \dfrac{Y}{10}\)
Test the relation Y² = XZ:
\(XZ = X \times \dfrac{Y}{10} = X \times \dfrac{X/10}{10} = \dfrac{X^2}{100}\)
\(Y^2 = \left(\dfrac{X}{10}\right)^2 = \dfrac{X^2}{100}\)
So \(Y^2 = XZ\).
Hence the correct relation is \(Y^2 = XZ\).
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