Question

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

Answer 1

Given:

• Rate = \(5\%\) per annum
• Time = 2 years
• Difference between Compound Interest (CI) and Simple Interest (SI) = ₹1125

Step 1: Let Principal be \( P \)

Compound Interest for 2 years at 5%: \[ \text{CI} = P \left(1 + \frac{5}{100}\right)^2 - P = P \left(1.1025 - 1\right) = P \cdot 0.1025 \]

Simple Interest for 2 years at 5%: \[ \text{SI} = \frac{P \cdot 5 \cdot 2}{100} = P \cdot 0.10 \]

Step 2: Use the given difference

\[ \text{CI} - \text{SI} = 1125 \Rightarrow P(0.1025 - 0.09) = 1125 \Rightarrow P \cdot 0.0125 = 1125 \Rightarrow P = \frac{1125}{0.0125} = \boxed{90000} \]

Final Answer:

✅ The Principal is: \[ \boxed{\text{₹ 90,000}} \]