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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
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: Aug 21, 2024
- 15
- 5
- 10
- 70
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The Correct Option is C
Approach Solution - 1
The equation \(10000 - 100x + 500x - 5x^2 \)
= 13500 can be solved to find its roots, which are x = 10 and x = 70.
Since x is less than 50, it can be concluded that x equals 10 percent.
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Approach Solution -2
If P is the whole investment, at the end of the first year, the investment's value is \(P(1 - x)\) due to a loss of x percentage.
The investment's value then rises by five times the following year.
\(P(1 - x)(1 + 5x)\) is the investment's total value as a result.
This is a 35% rise over the initial investment sum.
Thus, \(P = 1.35 P (1 - x)(1 + 5x) \)
Based on the available possibilities, we can observe that when \(x = 10\), the equation is satisfied.
Therefore The answer is 10.
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