Question : A sum of Rs. 2800 is divided into two parts in such a way that the interest on both parts is equal. If the first part is lent at 9% p.a. for 5 years and the second part is for 6 years at 10% p.a., find the two sums.
Option 1: Rs.1800, Rs.1000
Option 2: Rs.1600, Rs.1200
Option 3: Rs.1400, Rs.1400
Option 4: Rs.1300, Rs.1500
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Correct Answer: Rs.1600, Rs.1200
Solution :
Let the first part be $y$.
∴ Second part = Rs.$(2800 – y)$
According to the question,
Simple interest = $\frac{\text{Principal×Rate×Time}}{100}$
∴$\frac{y×5×9}{100}=\frac{(2800-y)×6×10}{100}$
⇒ $3y = 4 × 2800 – 4y$
⇒ $7y = 4 × 2800$
⇒ $y = \frac{4 × 2800}{7}$
⇒ $y = 1600$
∴ Second part = Rs. (2800 – 1600) = Rs.1200
Hence, the correct answer is 'Rs.1600 and Rs.1200'.
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