Question : The difference in simple interest on a certain sum at 6% per annum for 5 years and 5% per annum for 4 years is Rs. 422. Find the sum
Option 1: Rs. 2570
Option 2: Rs. 4220
Option 3: Rs. 6500
Option 4: Rs. 1990
Correct Answer: Rs. 4220
Solution :
Let the principal be $x$.
Rate = 6% for 1st case and 5% for 2nd case
Time = 5 years for 1st case and 4 years for 2nd case.
Difference = Rs. 422.
According to the question,
Difference in simple interest = $\frac{\text{Principal × Rate × Time}}{100}-\frac{\text{Principal × Rate × Time}}{100}$
⇒ $422 = \frac{x\times6\times5}{100}-\frac{x\times5\times4}{100}$
⇒ $422 = \frac{30x}{100}-\frac{20x}{100}$
⇒ $422 = \frac{10x}{100}$
⇒ $x=4220$
Hence, the correct answer is Rs. 4220.
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