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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