CAT 2022 Slot 2 QA Q18 Interest

Question 18 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

TITA: type in the answer. There are no options and no negative marking.

Answer: 20 Interest TITA

Solution

  1. The rest of the capital is \(1-\frac15-\frac13=\frac7{15}\).
  2. Yearly interest \(=\frac15(6\%)+\frac13(10\%)+\frac7{15}(1\%)=1.2\%+3.33\%+0.47\%=5\%\) of capital.
  3. Simple interest reaches 100% of the capital after \(100/5=20\) years.

Same concept in other years

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

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