[MeechMunchie]

I'm assuming the people who got it wrong did so because they calculated the second weight using the original water mass. As in, they used the amount of water in every 1% of the first set of watermelons to make up the 98% of the second without taking into account the overall decrease in mass i.e. each 1% is now smaller.

Haven't done maths in a couple of years, but here we go.

20/100 = 0.2 (The weight of every 1%)
0.2 x 99 = 19.8 (The weight of the water)

100 - 99 = 1 (How much is actually melon)
0.2 x 1 = 0.2 (The weight of actual melon)

*Thinks* Hmm. If I can't reconstruct the second weight using the values I have now, I'm stuck. Not sure. Heh, only 200g of that 20kg pile of watermelons is actually melon. That's funny. Wait a minute. Melon doesn't evaporate. Even if the percentages change, the mass of melon flesh will stay the same. I ma gemius!

100 - 98 = 2 (The percentage of melon that the same mass of flesh now makes)
0.2/2 = 0.1 (How much each 1% is therefore now worth weightwise)

0.1 x 98 = 9.8 (The weight of the remaining water)
9.8 + 0.2 = 1 (The total weight of water and flesh)

Turn that percentage back into the original units...

1 x 100 = 1kg

Now to hear why I'm completely and utterly wrong.

EDIT: Darn, that 1kg doesn't look right. I always lose something along the way...