Investment loss and growth percentage

CAT 2021 Slot 2 · QA · Medium · Profit & Loss

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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. A.

    15

  2. B.

    5

  3. C.

    10

  4. D.

    70

Answer

C

Explanation

Let L%L\% be the percentage loss in the first year. Growth percentage in second year = 5L%5L\%.

Overall gain over two years = 35%. Multiplication factor for net amount: (1−L100)(1+5L100)=1.35\left(1 - \frac{L}{100}\right) \left(1 + \frac{5L}{100}\right) = 1.35

Let x=L100x = \frac{L}{100}: (1−x)(1+5x)=1.35(1 - x)(1 + 5x) = 1.35 1+4x−5x2=1.351 + 4x - 5x^2 = 1.35 5x2−4x+0.35=05x^2 - 4x + 0.35 = 0 50x2−40x+3.5=050x^2 - 40x + 3.5 = 0 100x2−80x+7=0100x^2 - 80x + 7 = 0 (10x−7)(10x−1)=0(10x - 7)(10x - 1) = 0

So x=0.1x = 0.1 or x=0.7x = 0.7. L=10%L = 10\% or L=70%L = 70\%.

Since his balance after 1st year was strictly more than ₹ 5000: 10000(1−0.7)=3000<500010000(1 - 0.7) = 3000 < 5000 (rejected). 10000(1−0.1)=9000>500010000(1 - 0.1) = 9000 > 5000 (valid).

Thus, L=10%L = 10\%.

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