Multiple choice

Nitu has an initial capital of Rs. 20,000. Out of this, she invests Rs. 8,000 at 5.5% in bank A, Rs. 5,000 at 5.6% in bank B and the remaining amount at x% in bank C, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5% of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been

  1. 900

  2. 700

  3. 1,000

  4. 800
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total interest = 0.05 * 20000 = 1000. Interest from A = 8000 * 0.055 = 440. Interest from B = 5000 * 0.056 = 280. Interest from C = 1000 - (440 + 280) = 280. Remaining amount for C = 20000 - 8000 - 5000 = 7000. Rate x = (280/7000) * 100 = 4%. If all 20000 were in C, interest = 20000 * 0.04 = 800.

AI explanation

The remaining amount invested in bank C is 20000 minus 8000 minus 5000, which is Rs. 7000. Equating the total annual interest to 5% of 20000 gives (8000 times 0.055) plus (5000 times 0.056) plus (7000 times x divided by 100) equals 1000, which simplifies to 440 plus 280 plus 70x equals 1000. Solving for x gives 70x equals 280, so x equals 4. If the entire Rs. 20,000 were invested in bank C at 4%, the annual interest would be 20000 times 4 divided by 100, resulting in Rs. 800.

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