Multiple choice

Olivia has a total sum of Rs. 10,000, and she allocates it between two banks, A and B, in the ratio of 2 : 3. The rates of interest for these investments in Banks A and B, compounded annually, are in the ratio of 1 : 2. After two years, Olivia receives a total interest of Rs. 1,670. Determine the rate of interest for Bank A.

  1. 4%

  2. 5%

  3. 7%

  4. 8%

  5. 9%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Investment A = 4000, B = 6000. Let rate for A be r, then B is 2r. Interest = 4000((1+r)^2 - 1) + 6000((1+2r)^2 - 1) = 1670. Solving for r: 4000(2r + r^2) + 6000(4r + 4r^2) = 1670. 8000r + 4000r^2 + 24000r + 24000r^2 = 1670. 28000r^2 + 32000r - 1670 = 0. Solving gives r = 0.05 or 5%.

AI explanation

Let the principal for bank A be 2x and for bank B be 3x, and let the rate for bank A be r% so the rate for bank B is 2r%. Using the compound interest formula, the interest from bank A is 2x * [(1 + r/100)^2 - 1] and from bank B is 3x * [(1 + 2r/100)^2 - 1]. Testing r = 5, the interest from bank A is 2x * 0.1025 = 0.205x, and the interest from bank B is 3x * 0.21 = 0.63x, making the total interest 0.835x. Setting 0.835x equal to 1670 gives x = 2000, which makes the principals 4000 and 6000; this confirms the rate for bank A is 5%.

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