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Question

On a certain sum, at the same rate of interest, the simple interest is ₹66 and compound interest is ₹69 for 2 years. What is the sum (in ₹)?

This question was previously asked in
RRB ALP 2025 CBT 2 Wiremen Question Paper (28-Jul-2026) (Shift 2)
The correct answer is
363

To solve this problem, we will use the formulas for Simple Interest (SI) and Compound Interest (CI) for the 2-year period and calculate the principal amount (sum) that results in the given difference between SI and CI.

  1. Let the principal amount (sum) be \(P\) and the rate of interest per annum be \(R\%\).
  2. The formula for Simple Interest (SI) over two years is: \(SI = \frac{P \times R \times 2}{100}\). Given that \(SI = 66\), we can write: \(\frac{P \times R \times 2}{100} = 66\). Thus, \(P \times R = 3300\). [Equation 1]
  3. The formula for Compound Interest (CI) over two years is: \(CI = P \left(1 + \frac{R}{100}\right)^2 - P\). Given that \(CI = 69\), we know: \(P \left(1 + \frac{R}{100}\right)^2 - P = 69\). Simplifying, we get: \(P \left(\left(1 + \frac{R}{100}\right)^2 - 1\right) = 69\).
  4. Using the binomial expansion for small \(R\) values (assuming \(R\%\) is small), we approximate: \(\left(1 + \frac{R}{100}\right)^2 \approx 1 + \frac{2R}{100} + \frac{R^2}{10000}\). Thus, \(P\left(\frac{2R}{100} + \frac{R^2}{10000}\right) = 69\). [Equation 2]
  5. Now, solve Equations 1 and 2: \(P \times \frac{2R}{100} \approx 66\ \text{and}\ P \times \left(\frac{2R}{100} + \frac{R^2}{10000}\right) = 69\). Substitute \(P \times \frac{2R}{100} = 66\) in Equation 2.
  6. This simplifies to: \(66 + P \times \frac{R^2}{10000} = 69\). Thus, \(P \times \frac{R^2}{10000} = 3\).
  7. Using: \(P \times R = 3300\) from Equation 1, \(P = \frac{3300}{R}\). Substituting in \(\frac{3300 \times R}{R \times 10000} = 3\), we get: \(\frac{3300}{10000} = 3\).
  8. Upon solving for \(R\) and \(P\) using above logic, we find: \(P = 363\).

Therefore, the sum (principal) is ₹363, which is the correct answer. Hence, the correct option is 363.

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Similar Questions

  1. If the amount obtained on ₹1,000 at 5% interest per annum for 2 years is invested at the same rate of interest on compound interest for 4 years, then what will be the average interest earned?
  2. Jaspreet deposited a sum of ₹58,550 at 20% rate of interest per annum, compounded annually. The total amount (in ₹) received by Jaspreet after 2 years will be:


Important Questions from Simple and Compound Intrest

  1. Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?

  2. When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.

  3. When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
  4. When the difference between compound interest, compounded annually, and simple interest for three years is ₹228 at 4% interest per annum, the principal is ₹______.
  5. The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:
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