Multiple choice

Mrs. Rini Khan deposited Rs. X in a company at 17% per annum simple interest for 5 years and deposited an equal amount for fixed deposit in a bank 'A' for 4 years at 16% per annum simple interest. The interest from the company is Rs. 2,520 more than the interest from the bank. Mrs. Khan deposited Rs. (X + 8,000) in another bank 'B' at r% compound interest for 3 years. If after three years, Mrs. Khan received Rs. 26,620, find the compound interest on Rs. 25,000 at (r + 10)% for 2 years.

  1. Rs. 10,000

  2. Rs. 11,000

  3. Rs. 12,000

  4. Rs. 9,000

  5. Rs. 13,000
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B Correct answer
Explanation

From the interest difference: (X * 0.17 * 5) - (X * 0.16 * 4) = 2520, leading to 0.85X - 0.64X = 2520, so 0.21X = 2520, X = 12000. For bank B: (12000 + 8000) * (1 + r/100)^3 = 26620, so (1 + r/100)^3 = 1.331, meaning 1 + r/100 = 1.1, r = 10%. The compound interest on 25000 at 20% for 2 years is 25000 * (1.2^2 - 1) = 25000 * 0.44 = 11000.

AI explanation

The interest from the company is X multiplied by 17 multiplied by 5 divided by 100, and the interest from bank A is X multiplied by 16 multiplied by 4 divided by 100. Setting up the equation based on the difference gives 0.85X - 0.64X = 2520, which simplifies to 0.21X = 2520, resulting in X = 12000 rupees. The principal deposited in bank B is X + 8000, which equals 20000 rupees. Using the compound interest formula, 26620 = 20000 multiplied by (1 + r/100) cubed, which simplifies to (1 + r/100) = 1.1, meaning r is 10 percent. The required compound interest on 25000 at (10 + 10) = 20 percent for 2 years is calculated as 25000 multiplied by ((1.2 multiplied by 1.2) - 1), which equals 11000 rupees.

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