A store owner had 505 kg of fresh honeydews. The honeydews contained 60% water when fresh. One week later, there was only 50% water left in the honeydews. What was the mass of the honeydews one week later?

This depends on how you are measuring the water. This is one model:

0.60*505 = 303 kg water to start
If x kg of water was lost, then
(303-x)/(505-x) = 0.50
x = 101
so at the end of one week, the 404kg of melons contained 202 kg of water, and thus 1/3 of the initial water was lost.
If 1/3 of that was lost in the 2nd week, then the remaining water would be
303 * (2/3)^2 = 134.67 kg

-----------------------------
there are, naturally, other models that could be constructed. The best model would have to be determined by actual observation of honeydew populations.