Puzzle – Watermelons Drying in The Sun

Question: 

99% of a watermelon is water, 100 pounds of watermelon is available. After a week of sun drying, the shrivelled watermelon was only 98% dry. What is the watermelon’s current total weight?

Solution:

We see that initially, the weight of the watermelon was 100 pounds, which contained 99% water. This means that 99 pounds were water weight, and 1 pound was the weight of the dry matter of the watermelon, like the seeds and outer covering and inner flesh.

We need to find out the total mass of the watermelon after being shrivelled out by being kept under the sun for a week.

Let the final weight of the watermelon be W

The weight before and after drying up of the dry matter is the same = D_w = 1 pound

The final weight of water content will be (W_w) = Total Weight – Weight of Dry Matter = W – D_w

W_w = W – 1

We know that the watermelon is 98% dry.
Therefore, the weight of water content divided by the Initial weight is 0.98
 ⇒ W_w / W = 0.98
 ⇒ (W – 1) / W = 0.98                        (since W_w = W -1)
 ⇒ W – 1 = 0.98W
 ⇒ 0.2W = 1
 ⇒ W = 50

The final weight of the watermelon is 50 pounds, of which 1 pound is dry matter, and 49 pounds is the water weight.