Question:medium

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

Updated On: Jan 15, 2026
  • 15
  • 5
  • 10
  • 70
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The Correct Option is C

Solution and Explanation

To determine the solution, the percentage of loss incurred during the first year must be calculated. The following variables are defined:
  • Initial investment: ₹10,000
  • First year loss rate: x%
  • Second year growth rate: 5x%
  • Total profit over two years: 35%

First, calculate the amount remaining after the first year, accounting for an x% loss:

Y1=10000−x100×10000

This simplifies to:

Y1=10000−100x

The amount Y1 is then subjected to a 5x% growth in the second year:

Y2=Y1+5x×Y1100

Substituting the expression for Y1 yields:

Y2=(</mo>10000−100x)+5x×(</mo>10000−100x)100

The problem states that the total value after two years represents a 35% gain. Therefore:

(</mo>1.35×10000)=Y2

Substituting to solve for x:

13500=(</mo>10000−100x)+5x×(</mo>10000−100x)100

The equation is solved as follows:

13500=10000−100x+50x−5x×100x100

Combining like terms and solving for x yields:

13500=10000+59.5xSolving this yieldsx=10

Consequently, the percentage of loss in the first year is 10%.

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