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.
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.