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QB_GA_ADV_104
Question Bank • QB_GA_ADV_104
NAT • 2 Marks
Section 8: General Aptitude
Quantitative Aptitude
Subtopic: Numerical Computation
Question Statement:
The difference between the compound interest (compounded annually) and the simple interest on a certain principal sum invested for $3\text{ years}$ at an annual interest rate of $10\%$ is ext{Rs. }$930$. What is the principal sum in rupees? ________ (answer in integer).
Step-by-Step Solution & Explanation
**Method 1: Three-Year Interest Difference Formula**
For a 3-year investment at annual rate $r\%$:
$\text{CI} - \text{SI} = P \left[ 3\left(\frac{r}{100}\right)^2 + \left(\frac{r}{100}\right)^3 \right] = P \left[ \frac{r^2(300 + r)}{100^3} \right]$
Substituting $r = 10$ and $\Delta = 930$:
$930 = P \left[ \frac{100 \times 310}{1,000,000} \right] = P \times \frac{31}{1,000}$
$P = \frac{930 \times 1,000}{31} = 30 \times 1,000 = 30,000\text{ rupees}$
**Method 2: Verification**
- $\text{SI} = 30,000 \times 0.10 \times 3 = 9,000$.
- $\text{CI} = 30,000 \times (1.10)^3 - 30,000 = 30,000 \times 1.331 - 30,000 = 9,930$.
- $\text{Difference} = 9,930 - 9,000 = 930$.
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