Multiple choice

Sara invested a certain amount of money in two different schemes. In Scheme A, she earned \$1600 as simple interest after 2 years at 8% rate of interest. In Scheme B, she earned \$3570 as compound interest after 2 years. The rate of interest for Scheme B is 10% per annum. What is the ratio of the amount Sara invested in Scheme A to the amount she invested in Scheme B?

  1. 15 : 18

  2. 23 : 37

  3. 17 : 9

  4. 10 : 17
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D Correct answer
Explanation

For Scheme A: SI = 1600, R = 8%, T = 2 years. P = (1600*100)/(8*2) = 10000. For Scheme B: CI = 3570, R = 10%, T = 2 years. Amount = P(1 + 10/100)^2 = 1.21P. CI = 0.21P = 3570, so P = 3570/0.21 = 17000. Ratio = 10000 : 17000 = 10 : 17.

AI explanation

For Scheme A, we use the simple interest formula by rearranging it to find the principal, which gives 1600 divided by the product of 0.08 and 2, yielding 10000. For Scheme B, the principal equals the compound interest of 3570 multiplied by 100 and divided by the effective compound rate of 21, giving 17000. The ratio of the principal invested in Scheme A to Scheme B is 10000 to 17000, which simplifies to 10 to 17.

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