CAT 2022 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 9

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 9 : 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. 900
  2. 700
  3. 1000
  4. 800

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Explanatory Answer

If Neetu intended to get a 5% annual interest, ideally all the banks should have maintained a 5% interest rate.
But Bank A returns 0.5% extra interest on 8000 rupees, which is 40 rupees.
But Bank B returns 0.6% extra interest on 5000 rupees, which is 30 rupees.
A & B combines are paying 70 rupees extra than 5%.
So Bank C should maintain such an interest rate that, the interest generated on the remaining 7000 rupees is 70 less than 5% interest.
Since 70 is 1% of 7000. The interest rate at Bank C should be 5% - 1% = 4%
If all the 20,000 rupees were invested in Bank C, the interest generated is 4% of 20,000 = 800 rupees.

The answer is '800'

Choice D is the correct answer.

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