If I invest N2000 at x% and N2500 at y%, my annual income is N160. Had I invested N2500 at x% and N2500 at y%, my income would have been N155. Find x and y.

Let $x$ be the first percentage rate and $y$ be the second percentage rate. The income from an investment is calculated as (Amount $\times$ Rate) / 100.

From the first statement: "If I invest N2000 at $x\%$ and N2500 at $y\%$, my annual income is N160."

$$\frac{2000x}{100} + \frac{2500y}{100} = 160$$ $$20x + 25y = 160 \quad (1)$$

From the second statement: "Had I invested N2500 at $x\%$ and N2500 at $y\%$, my income would have been N155."

$$\frac{2500x}{100} + \frac{2500y}{100} = 155$$ $$25x + 25y = 155 \quad (2)$$

Subtract equation (1) from equation (2) to eliminate $y$:

$$(25x + 25y) - (20x + 25y) = 155 - 160$$ $$25x - 20x + 25y - 25y = -5$$ $$5x = -5$$ $$x = \frac{-5}{5}$$ $$x = -1$$

Substitute $x = -1$ into $20x + 25y = 160$:

$$20(-1) + 25y = 160$$ $$-20 + 25y = 160$$

Add 20 to both sides:

$$25y = 160 + 20$$ $$25y = 180$$ $$y = \frac{180}{25}$$ $$y = 7.2$$

The values are $x = -1$ and $y = 7.2$.

The final answer is $x = -1, y = 7.2$.