Multiple choice

A person divided a sum of Rs. 17,200 into three parts and invested these parts at 5%, 6% and 9% per annum simple interest. At the end of two years, he got the same interest on each part of money. What was the amount of money invested at 9%?

  1. Rs. 3,200

  2. Rs. 4,000

  3. Rs. 4,800

  4. Rs. 5,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let parts be P1, P2, P3. Interest: P1*0.05*2 = P2*0.06*2 = P3*0.09*2. So 0.05P1 = 0.06P2 = 0.09P3. P1 = 1.2P2, P3 = (0.06/0.09)P2 = (2/3)P2. P1 + P2 + P3 = 17200. 1.2P2 + P2 + 0.666P2 = 17200. 2.866P2 = 17200. P2 = 6000. P3 = (2/3)*6000 = 4000.

AI explanation

Let the three parts be x, y and z, and since they earn the same simple interest over two years, their principal amounts must be inversely proportional to their interest rates. The ratio of the parts is 1 divided by 5, 1 divided by 6, and 1 divided by 9, which simplifies to 18 to 15 to 10. The total of these ratio parts is 43, making the value of one part 17200 divided by 43, which is 400. The amount invested at 9 percent corresponds to 10 parts, so it is 10 multiplied by 400, giving a result of Rs. 4,000.

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