Question : A sum of Rs. 8,000 is divided into two parts. The simple interest on the first part, at a rate of 21% per annum, is equal to the simple interest on the second part, at a rate of 35% per annum. What is the interest (in Rs.) of each part?
Option 1: 1050
Option 2: 840
Option 3: 1400
Option 4: 1220
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Correct Answer: 1050
Solution :
Let the first part be $x$ and the second part be $(8000–x)$.
Simple Interest (SI) = $\frac{(\text{Principal × Rate × Time})}{100}$
The simple interests earned on both parts are equal.
Therefore, $\frac{(x × 21 × 1)}{100}=\frac{((8000–x) × 35 × 1)}{100}$
⇒ $21x=35(8000–x)$
⇒ $21x=280000–35x$
⇒ $56x=280000$
$\therefore x=5000$
Simple interest (SI) = $\frac{5000 × 21 × 1}{100}$ = $1050$
Hence, the correct answer is Rs. $1050$.
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