CAT 2022 Slot 3 QA Q9 Interest

Question 9 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

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 \(\mathrm{C}\), 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) 800 Interest MCQ

Solution

  1. Total interest \(=5\%\) of 20000 \(=1000\).
  2. Bank A: \(8000\times5.5\%=440\); Bank B: \(5000\times5.6\%=280\). So bank C gives \(1000-720=280\) on 7000, i.e. \(x=4\%\).
  3. Entire 20000 at 4%: ₹800.

Same concept in other years

See every question on Capital split across different interest rates: total interest.

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