Multiple choice

A person invested part of Rs. $4500$ at $4\%$ and the rest at $6\%.$ If his annual income from both are equal, then what is the average rate of interest?

  1. $4.6\%$
  2. $4.8\%$
  3. $5.0\%$
  4. $5.2\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the annual incomes from both parts are equal, the ratio of the investments is inversely proportional to their interest rates, giving P1 : P2 = 6% : 4% = 3 : 2. This means Rs. 2,700 is invested at 4% and Rs. 1,800 at 6%, yielding an annual income of Rs. 108 from each part. The total annual income of Rs. 216 on a total investment of Rs. 4,500 results in an average interest rate of (216 / 4500) * 100 = 4.8%.

AI explanation

Let the first part be x and the second part be (4500 - x), setting the interests equal gives 4% of x equals 6% of (4500 - x). Solving for x gives 0.04x = 270 - 0.06x, meaning 0.10x = 270, so x = Rs. 2700 and the other part is Rs. 1800. The total annual interest is 4% of 2700 plus 6% of 1800, which is 108 + 108 = Rs. 216, and dividing this by the total investment of 4500 gives an average rate of (216/4500) * 100 = 4.8%.

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