Potato Paradox

Initially : $99$ % of $100~pounds$ potato is water.

$\implies \text{Weight of water } = \dfrac{99}{100} \times 100 = 99~pounds$

$\text{Weight of remaining mass in potato (starch) } = 100 - 99 = 1~pound$

Finally : Now, only $98$ % of water is present. Let the new mass of potato be $x$ . Also, the mass of the of remainig potato (starch) remains same that is $1~pound$ .

$\text{Weight of water } = \dfrac{98}{100} \times x = \dfrac{49x}{50}$

Now, $\dfrac{49x}{50} + 1 = x$

$\implies 49x = 50x - 50 \implies \boxed{x = 50~pounds}$

Firstly, the 99%(i.e. 99 pound) of the potato was water, so the remaining 1 pound will be starch

After drying it the 1 pound becomes 2% of the potatoes

So this shows us that after drying 2% of potato=1 pound

Therefore 100% of potatoes = 50 pounds

Hence the answer is 50 pounds

99% of 100 is 99 which is water.

So there is 1 pound of potato.

Next day the potatoes are 98% water or 2% potato.

Therefore 1 is 2% of potato or 1 = .02 potato.

1/.02 = potato => 50 = potato.

Vsauce2 did it quite well. . Quite entertainingly as well.