My mother purchased 100 pounds of potatoes last week, which I knew to be exactly 99% water.

After a week, drying in the sun, they had dried a little to become only 98% water.

What was the total weight of the potatoes now?

[Ref: ZDMV]

50 pounds.

When the potatoes were originally bought they were 99% water, which weighed 99 pounds. So the potato part weighed 1 pound.

Once they had dried a little they were now 98% water and 2% potato. This 2% potato must still weigh 1 pound. This means that every 2% of the water also weighed 1 pound, which means there was 49 pounds of water and 1 pound of potato. A total of 50 pounds. QED.