## Hen Puzzle Redux

On a hot farm one day in July, 60% of the animals are hens. 70% of the animals are laying around, and 30% of the animals laying around are pigs. What is the maximum per cent of animals on the farm that could be hens laying around?

[submitted by a reader who liked this brain teaser]

Joe| Guest May 10th, 2007 - 11:59 pm49%

jason| Guest May 11th, 2007 - 7:26 ami’m thinking the other 70% of the animals laying around could be hens, or 82% of the total hens.

Carl| Guest May 11th, 2007 - 12:10 pmI’m sorta along with jason, but I have if 70% of the animals laying around are hens, then a maximum of 85.7% of the total animals could be hens laying around.

Adam| Guest May 11th, 2007 - 1:30 pmSince the remaining 70% of the 70% of animals laying only represents 49% of the total animals (less than 60% of the total hen population), we must say that there could be a maximum of 49% of the animals that are both hens and laying around.

Ree| Guest May 11th, 2007 - 4:05 pmI think it is 67% of the other animals could be hens…

the max percenage of other animals laying is 40% and the max % of the other animals being chicken is 60% so 40/60=67%

I think.

charity| Guest May 12th, 2007 - 12:09 ami think the answer is 42

pippa| Guest May 12th, 2007 - 5:08 am60%. ALL the hens could be laying down.

andrew hunt| Guest May 12th, 2007 - 9:42 amIf 30% of the animals laying around are pigs, then the other 70% of animals laying around must be hens. But 60% of the total amount of animals on the farm are hens. So 70% of that 60% are hens lying around, or .7 x .6 = 0.42 = 42%

andrew hunt| Guest May 12th, 2007 - 9:46 amNevermind, it’s 49%

inglewood| Guest May 12th, 2007 - 9:51 am49

nimrod| Guest May 12th, 2007 - 10:27 pm40%….i figure that’s as many hens that can lay around aside from the 30% which are pigs….

Prairie Kittin| Guest May 12th, 2007 - 11:05 pmBreaking this down to manageable numbers, let’s assume Old McDonald had 10 animals. Of these 10 animals, we know 6 of them are hens. (At least, in this puzzle, they are whole hens! I’m not even going to speculate on what he did with the half hens he had in the last puzzle!).

Now, 70% of these 10 animals are laying down, so 7 animals are laying down. 30% of these 7 are pigs. That means 2.1 of them are pigs. (What is with this guy and his portions of animals, anyway??). So, if 2.1 of the 7 animals are pigs, then the maximum amount of hens that could be laying is 4.9. Now, we’ve already established that he has 6 hens, so there are plenty of hens to fulfill this quota of 4.9 without having to disturb the horses, cows, and the rest of the animal population on this very weird farm.

So, 49% is maximum per cent of animals on the farm that could be hens laying around.

Prairie

Mjoller| Guest May 13th, 2007 - 4:48 amIf 60% are hens and 70% of the animals are layind down, then there is the possibility that ALL hens could be lying down. Now out of the 70%, 30% of them are pigs, so so the maximum % of chickens laying down could be 49%.

nimrod| Guest May 13th, 2007 - 4:02 pmsorry…didn’t read it right…i think it’s 49%…

jason| Guest May 14th, 2007 - 6:13 ammaybe i am not getting this right, but if 4.9 hens could be laying around, out of the total of 6 hens, that would be roughly 82% of the hen population.

Prairie Kittin| Guest May 14th, 2007 - 12:20 pmJason, The question was What is the maximum per cent of animals on the FARM, not the percentage of chickens.

nimrod| Guest May 14th, 2007 - 12:41 pmi’m confused….i’ll just stick to 40%….

nimrod| Guest May 14th, 2007 - 12:44 pmi got caught up in all the comments…..

jason| Guest May 15th, 2007 - 6:41 amthanks prairie, I misread the question. I had it stuck in me head they wanted the % of the hens….

charity| Guest May 26th, 2007 - 6:19 pmwait i think the answer is 70%

fantabulous| Guest May 28th, 2007 - 9:28 pm49%?

MJ| Guest June 24th, 2007 - 5:30 amNimrod, I don’t think you’re a nimrod. I think it’s 40% also. And to break it down into even more manageable numbers, similar to what Prairie did, I will say, on this farm there are 100 animals (100 percent of the animal population of the farm). 60 of these critters are hens.

Now, 70 of these 100 animals are laying around. 30 of those laying around are pigs. If you take away 30 from 70, you’re left with 40. This means that on this farm, there are 40 other animals laying around. This tells me that there is a possibility that a maximum of 40 lazy hens call this farm home. Several people on here have answered 49. I wish to test this theory using my example. Let’s say there are possibly 49 chickens laying around, along with the 30 pigs that are definitely laying around. 30 + 49 = 79. Wait a minute…. there’s only supposed to be 70 comatose animals here… Unless 9 hens avoided the census taker last year, it would be logically impossible for 79 of them to be laying around.

I say 40. “And that’s my final answer.”

Prairie Kittin| Guest June 24th, 2007 - 3:28 pmMJ…

You said that 70 of these 100 animals are laying around. 30 of those laying around are pigs. But, the puzzle didn’t say 30% of the entire population were pigs. The puzzle said that 30% of the *lazy* animals were pigs. Therefore, if 70 of the animals are lazy, then 30% of 70 = 21 of them were pigs. So, If 21 were pigs, then it stands to reason that 49 of the animals laying around were something other than pigs. Since there are 60 hens on the farm, that leaves plenty of room for all of the 49 to be pigs.

Prairie

MJ| Guest June 26th, 2007 - 4:53 pmWell Prairie…

It appears that I am certainly not at my best at 5:30 in the morning… You’re right. Guess I’m having crow for dinner tonight.

Pass the mustard?? :-)

Sarah Al Taher| Profile June 27th, 2010 - 8:47 amSimply it’s 40 %