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A sum of Rs P is invested for 3 years at 10% simple interest and earns Rs Q as interest. That interest Rs Q is then invested for 3 years at 10% simple interest and earns Rs R. Which relation holds?

1. Q = P + R
2. Q^2 = PR
3. P = Q + R
4. P^2 = QR

Correct answer: Q^2 = PR

Solution

With 3 years at 10%, the interest factor is 0.3, so Q = 0.3P and R = 0.3Q. Then PR = P*(0.3Q) = 0.3PQ while Q^2 = (0.3P)*Q = 0.3PQ, so Q^2 = PR.

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