Answer to Puzzle #47: Watermelons Drying in The Sun

47. Watermelon is 99% water. I have 100 pounds of watermelon. After a week, drying in the sun, the shrivelled watermelon had only dried down to being 98% water. What is the total weight of the watermelon now?

I don't know about you but I'm guessing it's going to be somewhere in the region of 99lbs plus or minus a little bit that we will calculate. Let's write it out:

picture of a watermelon to illustrate puzzleBefore reading the answer can I interest you in a clue?

Note the phrase 'had only dried down to' - this is trying to manipulate you in a certain direction. It is clearly trying to suggest the effect is small, which potentially stops you arriving at the answer which, in fact, comes from a large effect.

We can see, trivially, that at the beginning of the puzzle the 100lbs of watermelon has 1lb of dry matter and 99lbs of water. So the question, save a little finesse, becomes - what amount of water, when combined with 1lb of dry matter will be 98% water. Take a minute here to think about it. If you still can't get it, it is very possible that you are still being mislead by the deliberate misdirection in the question.

Explicit Solution

We are to determine X the total mass of melon after the drying.
The Dry weight, DW is 1lb both before and after the drying.
The New Water weight, WNW is clearly X - DW or X - 1

The set up tells us the New Water weight over the New total weight is 0.98 or 98%
WNW/X = 0.98
(X-1)/X = 0.98
X-1 = 0.98X
.02X = 1
X = 50

Which is the answer, 50lbs.

It's interesting how this puzzles manipulates you. When I asked earlier what amount of water, when combined with 1lb of dry matter will be 98% water, the answer, 49lbs is obvious. Now. If you got this one without having to work it out congratulations are due.

Assumptions

Assumptions in a puzzle like this are largely to do with the properties of watermelons, density at different temperatures etc. But of course there are no watermelons.





© Nigel Coldwell 2004 -  – The questions on this site may be reproduced without further permission, I do not claim copyright over them. The answers are mine and may not be reproduced without my expressed prior consent. Please enquire using the link at the top of the page.
 


PayPal
I always think it's arrogant to add a donate button, but it has been requested. If I help you get a job though, you could buy me a pint! - nigel

This Website Uses Cookies

Mostly, but not entirely to remember if you have dismissed this very box. Also to increase the functionality of the site. The cookies I apply do not uniquely identify you, by continuing to use this site you agree to let me place a cookie. I also have advert and analytics providers, for more information click here here.x