Question : The simple interest on a sum for 8 years is Rs. 47500. The rate of interest for the first 5 years is 10% per annum and for the next 3 years, 15% per annum. What is the value (in Rs.) of the sum?
Option 1: 50000
Option 2: 60000
Option 3: 45000
Option 4: 62500
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Correct Answer: 50000
Solution : Given: The simple interest on a sum for 8 years is Rs. 47500. Simple interest=$\frac{P\times R\times T}{100}$, where $P$ = Principal, $R$ = Rate of Interest, $T$ = time in years. According to the question, $47500=\frac{P\times 10 \times 5}{100}+ \frac{P \times 15 \times 3}{100}$ ⇒ $47500=\frac{50P}{100}+ \frac{45P}{100}$ ⇒ $47500=\frac{95P}{100}$ ⇒ $47500=\frac{19P}{20}$ ⇒ $P=\frac{47500\times 20}{19}$ ⇒ $P = 50000$ Hence, the correct answer is Rs. 50000.
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