Question

The difference between the compound interest and simple interest on a certain sum of money for 3 years at \(6\frac{2}{3}%\) per annum is ₹184, then what is the sum?

• A. ₹13500
• B. ₹12500
• C. ₹11500
• D. ₹10500

Hint:

For 3 years, \(CI - SI = P \left(\frac{r}{100}\right)^2 \left(3 + \frac{r}{100}\right)\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For 3 years, \(CI - SI = P \left[\left(1+\frac{r}{100}\right)^3 - 1 - \frac{3r}{100}\right]\).

Step 2: Detailed Explanation:
Rate \(r = 6\frac{2}{3} = \frac{20}{3}%\).
\(CI - SI = P\left[\left(1+\frac{20}{300}\right)^3 - 1 - \frac{3 \times 20/3}{100}\right]\)
\(= P\left[\left(1+\frac{1}{15}\right)^3 - 1 - \frac{20}{100}\right]\)
\(= P\left[\left(\frac{16}{15}\right)^3 - 1 - 0.2\right]\)
\(= P\left[\frac{4096}{3375} - 1.2\right]\)
\(= P\left[\frac{4096 - 4050}{3375}\right] = P \times \frac{46}{3375}\)
Given \(CI - SI = 184\), so \(P \times \frac{46}{3375} = 184\)
\(P = 184 \times \frac{3375}{46} = 4 \times 3375 = 13500\).

Step 3: Final Answer:
₹13500