Multiple choice

A man has part of $Rs. 4500$ invested at $4$% and the rest at $6$%. If the annual return on each investment is the same, the average rate of interest which he realizes on the $Rs. 4500$ is

  1. $5$%
  2. $4.8$%
  3. $5.2$%
  4. $4.6$%

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the amount at 4% and y be the amount at 6%. 0.04x = 0.06y. x + y = 4500. 0.04x = 0.06(4500-x) => 0.1x = 270 => x = 2700. y = 1800. Interest = 0.04(2700) + 0.06(1800) = 108 + 108 = 216. Average rate = 216 / 4500 = 0.048 = 4.8%.

AI explanation

Let the sum invested at 4% be x, so the sum invested at 6% is (4500 - x). Since the annual returns are equal, 4% of x equals 6% of (4500 - x), meaning 0.04x = 0.06(4500 - x). Solving this gives 0.1x = 270, so x is 2700 invested at 4% and 1800 invested at 6%. The total annual interest is 108 + 108 = 216, and the average rate of interest is (216 / 4500) * 100 = 4.8%. The average rate realized is 4.8%.

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