A Trivial Question - Increasing by doubling a number when its negative 

The question is : if $x=y-\frac{50}{y}$ , where x and y are both > $0$ . If the value of y is doubled in the equation above the value of x will a)Decrease b)remain same c)increase four fold d)double e)Increase to more than double -  Ans)e


Here is how I am solving it $x = \frac{y^2-50}{y}$ by putting y=$1$ .  I get $-49$ and by putting y=2(Doubling) I get $y=-24$. Now how is $-24$ more than double of $-49$. Correct me if I am wrong double increment of $-49$ will be = $-49+49 = 0$ which would be greater than -24.

Let $x_1=y-\frac{50}{y}$ and $x_2=2y-\frac{50}{2y}$. Then $x_2-x_1=(2y-y)-(\frac{50}{2y}-\frac{50}{y})=y+\frac{50}{2y}=y-\frac{50}{y}+(\frac{150}{2y})=x_1+(\frac{150}{2y})$
$\implies x_2-2x_1=(\frac{150}{2y})\gt 0$ (as $y\gt 0$)$\implies x_2\gt 2x_1\implies x_2/x_1\gt 2$ which is option (e).
