Question : A certain sum (in INR) is invested at simple interest at y% per annum for $3 \frac{1}{2}$ years. Had it been invested at (y + 4)% per annum at simple interest, it would have fetched INR 4,452 more as interest. What is the sum?
Option 1: INR 42,400
Option 2: INR 31,800
Option 3: INR 30,400
Option 4: INR 42,800
Correct Answer: INR 31,800
Solution :
Given:
Time, $t\ = 3\tfrac{1}{2}$ years
Original rate = $y\%$
New rate = $y\ +\ 4\%$
Let the principal be INR $x$.
According to the question,
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
$\Rightarrow \frac{x\ \times (y\ +\ 4\ -\ y)\times 7}{100\ \times 2} = 4452$
$\Rightarrow \frac{x\ \times 4\times 7}{100\ \times 2} = 4452$
$\Rightarrow x\ = \frac{4452\times 2\times 100}{4\times 7}$
$\Rightarrow x\ = 31800$
Hence, the correct answer is INR 31,800.
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