The sum of two positive numbers is 20% of the sum of their squares and 25% of the difference of their squares. If the numbers are x and y the, $$\ \frac{x+y}{x^{2}}\ $$ is equal to

Given x+y $$= \frac{20}{100}\times(x^{2}+y^{2})$$

$$\Rightarrow$$ x+y $$= \frac{1}{5}\times(x^{2}+y^{2})$$

$$\Rightarrow$$ $$x^{2}+y^{2} =$$ 5(x+y) $$\rightarrow$$ (1)

Also Given x+y $$= \frac{25}{100}\times(x^{2}-y^{2})$$

$$\Rightarrow$$ x+y $$= \frac{1}{4}\times(x^{2}-y^{2})$$

$$\Rightarrow$$ $$x^{2}-y^{2} =$$ 4(x+y) $$\rightarrow$$ (2)

Adding equation(1) and equation(2)

$$\Rightarrow$$ 2x$$^{2} =$$ 9(x+y)

$$\therefore$$ $$\frac{x+y}{x^{2}} = \frac{2}{9}$$