Question : If the simple interest on a certain sum of money is INR 11,220 at the rate of $16 \frac{1}{2} \%$ per annum for 8 years and 3 months, then what is the principal amount (in INR, rounded off to the nearest rupee)?
Option 1: 4,228
Option 2: 6,822
Option 3: 8,422
Option 4: 8,242
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Correct Answer: 8,242
Solution : Simple interest (SI)= $\frac{\text{Principal × Rate × Time}}{100}$ SI = INR 11,220 Rate = $16\frac{1}{2}$ = $\frac{33}{2}$% Time = 8 years 3 months = $8\frac{3}{12}$ = $8\frac{1}{4}$ = $\frac{33}{4}$ According to the question, 11220 = $\frac{\text{P×33×33}}{100×2×4}$ ⇒ P = $\frac{11220×800}{1089}$ = $\frac{8976000}{1089}$ = 8242.424 = 8242 Approx Hence, the correct answer is 8,242.
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