BrainDen.com - Brain Teasers

## Question

Fred has 100 lbs of potatoes which consist of 99 percent water.  Leaving them outside overnight, Fred finds his potatoes only consist of 98 percent water.  What is their new weight?  What was the weight of the 1% of water lost?  What is the weight of the 98% water remaining?

## Recommended Posts

• 0

Problems like this always SEEM so straightforward, but the answers are always a little shocking to see:

New weight: 50lbs
Weight of the 1% water lost: 50lbs
Weight of the 98% water remaining: 49lbs

First let's do the obligitory/obvious initial analysis of the original amounts:

0.99 = water weight / total weight

0.99 = water weight / 100

water weight = 99lbs

So, now we need to find the new weights:

0.98 = new water weight / new total weight

we know that the new water weight is: 99 - water weight lost

and we know the new total weight is: 100 - water weight lost

Let x = water weight lost

This gives us the equation:

0.98 = (99 - x) / (100 - x)

98 - .98x = 99 - x

0.02x = 1

x = 50

This means the water weight lost was 50lbs...so using that, we can find the answers above. We can certainly validate this answer by showing that if we have 50lbs of potatoes, and 49lbs of it are water, we indeed have 98% water weight, and both the total weight and water weight decreased by the same amount (50lbs)...or another way of seeing that is that the original weight of the non-water parts of the potatoes were 1 pound (100 - water weight)...since that does not change after the water evaporates overnight, the end result should still have 1 pound of non-water weight...which we do have (50 - 49).

Edited by Pickett

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account. ×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×