Question : The simple interest on a certain sum at the rate of 12.5% per annum for 6 years is INR 13,500 less than the principal. Find the simple interest.
Option 1: INR 13,500
Option 2: INR 54,000
Option 3: INR 40,000
Option 4: INR 40,500
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Correct Answer: INR 40,500
Solution : Let the principal be $p$. We know, $\frac{\text{Principal × Rate × Time}}{100}$ = Simple interest ⇒ $\frac{\text{Principal × Rate × Time}}{100}$ = Principal amount – 13500 ⇒ $\frac{p × 6 × 12.5}{100} = p - 13500$ ⇒ $\frac{75p}{100} = p - 13500$ ⇒ $3p = 4 × (p - 13500)$ ⇒ $p = 54000$ The simple interest is (54,000 – 13,500) = INR 40,500 Hence, the correct answer is INR 40,500.
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