In a world where water dances with organic hues, our heroes, alum, and lime$,$ step onto the stage, ready to perform their magical act of color extraction! Imagine this: five parts of alum and lime per million parts of water diminish the color to a modest $20\%$ of its former glory. But wait, there's more! With ten parts, they delve deeper, reducing the color to a mere $5\%.$

Now, our daring quest: estimate the precise concoction of alum and lime$,$ in parts per million, needed to diminish the color to a scant $1\mathrm{.}0\%$ of its original vibrancy.

So$,$ dust off your chemistry capes and sharpen your $15$ arithmetic wits! Let's embark on this chromatic adventure and paint the town clear!

Round your answer to $2$ decimal places.