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

• A. 15
• B. 5
• C. 10
• D. 70

Answer 1

The Correct Option is C

To solve the problem, we need to find the percentage of loss in the first year. Let's define the variables:

• Initial investment amount = ₹10,000
• First year's loss percentage = x%
• Second year's growth percentage = 5x%
• Total gain over two years = 35%

First, calculate the amount remaining after the first year with a loss of x%:

$\mathrm{Y1}=10000-\frac{x}{100}\times 10000$

Rearranging gives:

$\mathrm{Y1}=10000-100x$

The amount Y1 is invested for another year and grows by 5x%:

$\mathrm{Y2}=\mathrm{Y1}+\frac{5x\times \mathrm{Y1}}{100}$

Substituting for Y1 from above, we have:

$\mathrm{Y2}=\left(100x\right)+\frac{5x\times 100x}{100}$

According to the problem, the total value after 2 years represents a 35% gain. Therefore:

$(1.35\times 10000)=\mathrm{Y2}$

Substituting to solve for x:

$13500=(10000-100x)+\frac{5x\times (10000-100x)}{100}$

Solving:

$13500=10000-100x+50x-\frac{5x\times 100x}{100}$

Combine like terms and solve for x:

$13500=10000+59.5x\text{Solving this gives}x=10$

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

Answer 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.