SOLUTION: A person invest 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 s

Question 1118615: A person invest 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.The ratio of his investments is :
A)2:3:4 B)3 :4 :2 C)3: 4: 6 D)6 :3 :2
Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

Note that, with the multiple choice answer choices, common sense says the answer has to be D. The investment at the lowest interest rate was for the shortest amount of time, and the investment at the highest interest rate was for the longest amount of time. Clearly, if the amounts of interest from all three investments are the same, the largest amount has to be at the lowest rate and the smallest amount at the highest rate. Only answer choice D satisfies those requirements.

But let's look at the details of a formal solution.

(1) 6 years of 10% simple interest earns interest in the amount of 60% of the amount invested.
(2) 10 years of 12% simple interest earns interest in the amount of 120% of the amount invested.
(3) 12 years of 15% simple interest earns interest in the amount of 180% of the amount invested.

The percentages of the interest from the three investments are in the ratio 60:120:180 = 1:2:3.

Then, for the amounts of interest from all three to be the same, the amounts invested have to be in the "reciprocal ratio": (1/1):(1/2):(1/3), or 6:3:2. Answer D.

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