Multiple choice

Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

  1. 62.5%

  2. 37.5%

  3. 60%

  4. 40%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the two parts of the investment be P1 and P2. The simple interest on the first part is P1 * 0.15 * 4 = 0.60 * P1, and on the second part is P2 * 0.12 * 3 = 0.36 * P2. Equating the two interests gives 0.60 * P1 = 0.36 * P2, which simplifies to the ratio P1 / P2 = 3 / 5. Thus, the percentage of savings in the first part is 3 / (3 + 5) = 37.5%.

AI explanation

Using the simple interest formula, the interest on the first part is P1 times 15 times 4 divided by 100, and the interest on the second part is P2 times 12 times 3 divided by 100. Equating the two yields 0.60P1 equals 0.36P2, so P2 equals 1.6667P1. The total savings is P1 plus P2, which is 2.6667P1; the percentage invested in the first part is (P1 divided by 2.6667P1) times 100, making the result 37.5%.

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