Question : A sum was lent at simple interest at a certain rate of 2 years. Had it been lent at a 3% higher rate, it would have fetched Rs. 300 more. The original sum of money was:
Option 1: Rs. 5000
Option 2: Rs. 6000
Option 3: Rs. 7000
Option 4: Rs. 4000
Correct Answer: Rs. 5000
Solution :
Given: A sum was lent at simple interest at a certain rate of 2 years. Had it been lent at a 3% higher rate, it would have fetched 300 more.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
Let the rate be $R$% and the increased rate be $(R+3)$%.
So, $\frac{P\times (R+3) \times 2}{100}-\frac{P \times R \times 2}{100}= 300$
⇒ $\frac{P \times 2}{100}×(R+3-R) = 300$
⇒ $\frac{P\times 2\times 3}{100} = 300$
$\therefore P =$ Rs. 5000
Hence, the correct answer is Rs. 5000.
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