CAT 2021 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 18

CAT 2021 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 18 : Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is

  1. 15
  2. 5
  3. 10
  4. 70

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Explanatory Answer

Let the total investment be P, then at the end of the first year, after a loss of x percentage the value of the investment becomes
P(1 - x)
Then in the next year the value of the investment increases by 5x
So, the overall value of the investment becomes
P(1 - x)(1 + 5x)
This is an increase of 35% from the initial investment amount.
1.35 P = P (1 - x)(1 + 5x)
Going by the options we can see that the equation is satisfied when x = 10
Hence 10 is the answer

The answer is '10'

Choice C is the correct answer.

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