Question : The simple interest on an amount for 6 years at 4% p.a. is 7,500 less than the simple interest on the same amount for 11 years. Find the amount (in Rs.).
Option 1: 38,000
Option 2: 37,500
Option 3: 37,000
Option 4: 38,500
Correct Answer: 37,500
Solution :
Given: Rate = 4% for both cases
Time = 6 years for 1st case and 11 years for the second case.
Let the amount be P.
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
According to the question,
⇒ $\frac{\text{P × 4 × 11}}{100}–\frac{\text{P × 4 × 6}}{100} = 7500$
⇒ $\frac{\text{44P}}{100}–\frac{\text{24P}}{100} = 7500$
⇒ $\frac{\text{20P}}{100} = 7500$
⇒ P = Rs. 37,500
Hence, the correct answer is 37,500.
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