Question : The simple interest on a certain sum of money for 2 years at 7% per annum is double the compound interest on INR 1,000 for 2 years at 10% per annum, compounded annually. What is the sum placed on simple interest?
Option 1: INR 1,000
Option 2: INR 2,000
Option 3: INR 3,000
Option 4: INR 4,000
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Correct Answer: INR 3,000
Solution : Simple interest on a certain sum of money for 2 years at 7% per annum = 2 × compound interest on INR 1,000 for 2 years at 10% per annum According to the question, $\frac{P_1nR}{100}= 2 × [P_2(1+\frac{R}{100})^n - P_2]$ Here $P_1$ is the principal for simple interest and $P_2$ is the principal for compound interest. So,$\frac{P_1×2×7}{100}= 2 × [1000(1+\frac{10}{100})^2 - 1000]$ ⇒ $\frac{14P_1}{100}= 2 × [1000(\frac{11}{10})^2 - 1000]$ ⇒ $\frac{14P_1}{100}= 2 × 1000×(\frac{121}{100}-1)$ ⇒ $\frac{14P_1}{100}= 2 × 1000×\frac{21}{100}$ ⇒ $P_1 = \frac{42000}{14}=3000$ Hence, the correct answer is INR 3,000.
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