Simple Interest Investments

CAT 2022 Slot 3 · QA · Easy · Arithmetic

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Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in bank A, ₹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. A.

    900

  2. B.

    700

  3. C.

    1000

  4. D.

    800

Answer

D

Explanation

Total capital =20,000= 20,000.

  • Bank A investment =8,000= 8,000 at 5.5%  ⟹  InterestA=8000×0.055=4405.5\% \implies \text{Interest}_A = 8000 \times 0.055 = 440.
  • Bank B investment =5,000= 5,000 at 5.6%  ⟹  InterestB=5000×0.056=2805.6\% \implies \text{Interest}_B = 5000 \times 0.056 = 280.
  • Remaining amount in Bank C =20,000−8,000−5,000=7,000= 20,000 - 8,000 - 5,000 = 7,000.

Total desired interest =5%= 5\% of 20,000=1,00020,000 = 1,000.

Interest from Bank C =1000−(440+280)=1000−720=280= 1000 - (440 + 280) = 1000 - 720 = 280. Interest rate x%x\% of Bank C: 7000×x100=280  ⟹  x=4%7000 \times \frac{x}{100} = 280 \implies x = 4\%.

If the entire 20,00020,000 were invested in Bank C at 4%4\% per annum, annual interest income would be: 20000×0.04=80020000 \times 0.04 = 800

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