Fruity paradox

Algebra Level 2

In the magical world of Fruity Land, there exists a giant fruit that is made up of 99.95% water and 0.05% solid matter (minerals, vitamins, carbs, seeds, and other materials). An explorer picked lots of these fruits so that he could eat some and bring the rest back to his homeland. However, the fruits were very heavy, weighing 200 pounds in total. Even with his ox, it was a long and grueling trip back to his house. It took so long that he needed to rest for one night. Overnight, some of the water evaporated from the fruits, leaving the fruits with 99.9% water and 0.1% solid matter. The next day, the explorer continued traveling but was surprised to find how quickly he had gotten to his house.

What was the new total weight of the fruits, in pounds?

This problem was inspired by a video on Vsauce2.

The answer is 100.

3 solutions

Zee Ell
Mar 27, 2018

The weight of solid matter = 200 pounds × 0.05 % = 0.1 pounds

The new weight of the fruits:

$0.1 \text { pounds } ÷ 0.1 \% = \boxed { 100 \text { pounds } }$

But the problem states the fruits were made up of 99.95% of water and 0.05% of solid matter and that some of it had evaporated overnight. How can the water within the fruit possibly increase to 99.99% after some of it evaporated out of it? I do not understand this at all.

Simon The Great - 3 years, 2 months ago

Its not 99.99% but its 99.9%(which is less than 99.95%). Is this problem cursed?

Manurag M - 3 years, 2 months ago

Manurag M
Mar 27, 2018

The wight of matter = 200x0.05%=10 pounds.
The 10 pounds now become the 1%.
Thus mass = 10/0.1=100 pounds.

When you multiply something by 0.05%, that's multiplying it by 0.0005, because it's a percentage. So the weight of the matter is 0.1 pounds.

Joseph Newton - 3 years, 2 months ago

You are right . sorry for the mistake and thank you for teaching.

Manurag M - 3 years, 2 months ago

Philippe Lê
Mar 27, 2018

Let $x$ be the loss in pounds of water, $p$ and $p'$ the former and new proportions of water respectively.

The new mass of water : $200p - x$ .
The new mass of the fruits : $200 - x$ .
Hence, the new mass of water needs to be equal to $(200 - x)p'$ .

Then, solving the following equation for $x$ : $200p - x = (200 - x)p'$

gives $x = \frac{200p - 200p'}{1 - p'}$ , which is equal to $100$ . Hence $200 - 100 = 100$ pounds is the new total weight of the fruits.

Fruity paradox

The answer is 100.

3 solutions

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