Multiple choice

A person invests money in three different schemes for $6$ years, $10$ years and $12$ years at $10\%,12\%$ and $15\%$ simple interest respectively. At the completion of each scheme, he gets the same interest. What is the ratio of his investments?

  1. $\;6\,\colon\,3\,\colon\,2$.
  2. $\;2\,\colon\,3\,\colon\,4$.
  3. $\;5\,\colon\,2\,\colon\,1$.
  4. $\;7\,\colon\,4\,\colon\,2$.
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A Correct answer
Explanation

Let investments be I1, I2, I3. Interest is equal: I1*0.10*6 = I2*0.12*10 = I3*0.15*12. 0.6*I1 = 1.2*I2 = 1.8*I3. Dividing by 0.6: I1 = 2*I2 = 3*I3. Ratio I1:I2:I3 = 1 : 1/2 : 1/3 = 6 : 3 : 2.

AI explanation

Since the simple interest (P x R x T)/100 is the same for all three schemes, the investments are inversely proportional to the product of the rate and time. The product for the first scheme is 6 x 10 = 60, for the second is 10 x 12 = 120, and for the third is 12 x 15 = 180. The ratio of investments is the inverse ratio of these products, 1/60 : 1/120 : 1/180, which becomes 6 : 3 : 2 when multiplied by 360.

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