Multiple choice

Sonali invests money in three different schemes for 6 years, 10 years and 12 years at 10% p.a. 12% p.a. and 15% p.a. at simple interest, respectively. At the completion of each scheme, she gets the same interest. What is the ratio of her investments?

  1. 6 : 3 : 2

  2. 3 : 2 : 1

  3. 3 : 4 : 5

  4. 2 : 3 : 6
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A Correct answer
Explanation

Interest = P * R * T / 100. Since interest is equal, P1*10*6 = P2*12*10 = P3*15*12. This gives 60*P1 = 120*P2 = 180*P3. Dividing by 60, we get P1 = 2*P2 = 3*P3, so the ratio P1:P2:P3 is 6:3:2.

AI explanation

Since the simple interest from all three schemes is equal, the products of the rate, time, and principal must be identical. This means the principal for each scheme is inversely proportional to the product of its rate and time. Calculating these products gives 60, 120, and 180, and finding the inverse ratio gives 1/60 : 1/120 : 1/180. Multiplying by the least common multiple of 360 gives the ratio 6 : 3 : 2, making the result 6 : 3 : 2.

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