Watermelons Drying in The Sun

A farmer is proud of his newest feat: growing a 120 kg watermelon that he wants to enter in the farming contest next week. Using a special sensor, he detects that the watermelon is 99% water by mass.

However, one day the wind blows off the tarp sheltering the watermelon, leaving it out in the sun to shrivel up and lose some of its water content. The farmer is devastated.

“The watermelon is ruined! I can’t enter it in the contest!”

“Why not?” his wife replies.

The farmer uses the sensor. “You see? It’s only 98% water now.”

“That’s still pretty heavy.”

“You don’t understand. Mr. Jones next door has a 100 kg watermelon. This won’t do at all.”

How heavy is the farmer’s watermelon now?

Solution

The watermelon is only 60 kg heavy now.

At the start, the watermelon consists of 99% of water by mass. This means that the non-water parts of the watermelon is $1\%\times 120\text{ kg}=1.2\text{ kg}$1%×120 kg=1.2 kg.

After losing some of its water content, the 1.2 kg is now 2% of the watermelon’s weight, which works out to only 60 kg for watermelon’s full weight.