cat 2021 Question 18

Question

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

Accepted Answer

Raj invested Rs 10000 in the first year. Assuming the loss he faced was $x\%$.

The amount after 1 year is $10000(1 - x/100) = 10000 - 100x$.

Given the balance was greater than Rs 5000 and hence $x < 50$ percent.

When Raj invested this amount in the second year he earned a profit which is five times that of the first-year percentage.

Hence the amount after the second year is: $(10000 - 100x)\left(1 + \frac{5x}{100}\right)$.

Raj gained a total of 35 percent over the period of two years and hence 35 percent is Rs 3500.

Hence the final amount is Rs 13,500.

$(10000 - 100x)\left(1 + \frac{5x}{100}\right) = 13500$

$(100 + 5x)(100 - x) = 13500$

$10000 - 100x + 500x - 5x^2 = 13500$

$5x^2 - 400x + 3500 = 0$

Solving the equation, the roots are:

$x = 10,\ x = 70$.

Since $x < 50$, $x = 10$ percent.

Question 18.

Question Explanation