Question : The difference between compound interest and simple interest on Rs. X at 7.5% per annum for 2 years is Rs. 22.50. Find the value of X.
Option 1: Rs. 4000
Option 2: Rs. 5000
Option 3: Rs. 2000
Option 4: Rs. 1900
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Correct Answer: Rs. 4000
Solution : Given: Principal = Rs. X Rate = 7.5% Time = 2 years The difference between compound interest and simple interest, D = Rs.22.50 We know that, $D=P(\frac{r}{100})^2$ ⇒ $22.50=X(\frac{7.5}{100})^2$ ⇒ $22.50=X(\frac{3}{40})^2$ ⇒ $22.50=X\times\frac{3}{40}\times\frac{3}{40}$ ⇒ $X=1600\times2.5$ ⇒ $X=4000$ Hence, the correct answer is Rs. 4000.
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