Discussion
A man has ₹ 9,000 to invest. He invests ₹ 3,500 at 6% per annum simple interest and ₹ 3,000 at 5% per annum simple interest. In order to have a yearly income of ₹ 450, at what rate must he invest the remaining amount ?
Answer: A
He must invest the rest at 3.6% per annum.
Interest from the first two investments, and the amount left:
\[ \begin{aligned} 3500 \times 6\% &= 210 \\ 3000 \times 5\% &= 150 \\ \text{remaining} &= 9000 - 6500 = 2500 \\ \text{needed} &= 450 - 360 = 90 \\ \text{rate} &= \frac{90}{2500} \times 100 = 3.6\% \end{aligned} \]
3.5%, 3.8% and 3.9% would give yearly incomes of 87.50, 95 and 97.50 rupees from the remaining 2,500, so the total would not be exactly 450.
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