I Told You I Was Ill
A hypochondriac drinks his medicine until there is only one third left in the bottle. He then dilutes the rest with water until the bottle is two thirds full.
"This would be too light" he said to himself and tops the bottle with a mixture twice as strong as the original medicine.
He is still not sure if the resultant mixture is stronger or weaker than the original one, and by how much. Are you ?
"This would be too light" he said to himself and tops the bottle with a mixture twice as strong as the original medicine.
He is still not sure if the resultant mixture is stronger or weaker than the original one, and by how much. Are you ?
posted by Rajesh Lal at
8:47 PM
21 Comments:
It is the same concentration as the original mixture
~Cybersurf~
Indeed it is the same strength and for this reason. He drank 2/3 of the medicine. Filling the bottle only 1/3 that leaves 1/3 left remaining in the bottle. Adding the addition 1/3 of double medicine strength would be just like adding 2/3 regular medicine which would make the medicine the same strength as was its original dosage.
I say its weaker. you still have to account for the 1/3rd of the bottle thats water. so if you take the regular strength 1/3rd and add the double strength 2/3rd which would make it a full strength bottle 3/3rds but there is still 1/3rd of water in the bottle which would dilute the entire bottle.
c.r.s.
He is a hypochondriac its the same because his "medicine" is water anyhow.
Drake
It will be dilute by 1/6th...
It would be stronger...
Lets say x is the strength / potency in the bottle... so we have:
1/3 of x diluted into half as 1/3 part of water is added therefore the mixture is 1/6 of x
We then add 1/3 part medicine twice as potent
We have 2/3 of x which should all add up to one
2x/3 + 1x/6 = 1
> 5x/6 = 1
> x = 6/5
therefore the potency in the bottle is more than what we initially started with...
I agree with c.r.s.
1/3 of the new mixture is double strength, the other 2/3 is half as strong as the original mixture, therefore the resulting mixture is weaker. If it had been filled to half way then topped up with double strength mixture it would be the same but more water was added and less double strength mixture.
I'm unsure though why the fact that he is a hypochondriac is relevant. He would then still be taking genuine medicine but might not be as ill as he thinks he is?
i would say it is the same... bascially there are 3 solutions.. the 1 part original medicine, 1 part double the strength and 1 part water... taking that the final strength does not depends on the order of mixing... if you mix the 1 part water with 1 part double strength medcine.. you would dilute it by half thus the strength should be the same as the original and hence the final mixture is no different from the original med..
It is not double strength, it is the same for this reason:
Suppose you have his bottle and let's call it 1. Subtract 2/3 from 1 and you have 1/3. Seeing as how it's water, it's strength will still be that of the 1/3, should he drink the whole thing at once. So he dilutes 036$the medicine to 2/3, which will be as strong as 1/3 should he drink the entire thing, weaker if not. When he tops it off, he uses double strength. So we have 1/3 of another bottle with twice the strength. We're back at 1, right? The 1/3 double is the same strength as 2/3 normal because 1/3 x 2/1 = 2/3. So when he adds the double strength 1/3 of the strength is the top-off and 1/3 is reinforcing the diluted 1/3.
1/3 + 1/3 + 1/3 = 1.
There the same strength.. let's look at it as percentages..
33.33%*full + 33.33%*none + 33.33% * 2
.3333 * 1 + .3333 * 0 + .3333 * 2 =
.3333 + .6666 = .9999
or.. consider 1/3 bottle at normal and 1/3 bottle water is 2/3 at half strength.. back to percentages now..
.6666 * .5 + .3333 * 2 =
.3333 + .6666 = .9999
It is the same strength. Substitute x for a 1/3 at regular strength. Starts with 3x. Drinks 2 x,leaves 1 x. Adds water to fill to 2/3 but still has only 1x diluted into but in 2/3's full bottle. Adds 2x in the space of 1/3 - bottle is full and he has 3x of medicine.
Its weaker...
You have, to start with, 1/3 potency which is diluted in half which results in 1/6 potency. To this if you add 2/3 of potency you still get only 5/6 of the potency... the mixture is therefore weaker by 1/6 in potency...
it is the same because DUNNO it is just a guese
POTTER- i cannot see the 1/6 weaker idea, you are changing the original fraction. the potency, after adding the water would be half. 3/6. adding the double potency medicine, which would be a 2/1 fraction, would account for the zero strength water that was added. the result is a bottle of the same potency. trust me, i've taken chemistry and passed with an A
Hi everyone. The answer is that the bottle would have the same potency as the original. The thing is, the starting potency would still be the same even if he drank it til its 1/3 full. For example: The original medicine is 9 Liters which is a 90% concentrated. He drank 6 Liters of it which leaves it to 3 Liters, 90% concentrated. He added 3 Liters of water,0% concentrated (to make the bottle 2/3 full) and made the solution to 6 Liters again, which is 45% concentrated. Lastly, he added another 3 Liters but this time, it is 180% concentrated of medicine(twice as strong). The final solution will then be 9 Liters again, which is still 90% concentrated.
1/3 is 100%
1/3 is 0%
and
1/3 is 200%
Adding up the products gives 100%. So it is now back at the original strength.
But since, he's a hypochondriac, the doctor has prescribed 0% strength, it was all just flavored water anyway, but the flavoring is back at 100%. LOL.
hjg
The first one is stronger
The 2nd one is 1/3rd + 1/3rd of twice strength so thats 2/3rds.. which is the same strength! BUT... he has also added 1/3rd water to the second concentration meaning its actually weaker considering the volume is the same.
It's obviously the "SAME" concentration!
Original potency = x,
(So (1/3)x
remains in the bottle.)
Adding 1/3 at double potency = 2x
However the prior 1/3 water (no potency) + the 2x makes each of those 1/3 additions have a potency = x each.
Therefore with each (1/3) portion of mixture have an equal potency of "x" you get the an easy equation of:
(1/3)x + (1/3)x + (1/3)x = (3/3)x or simply = x.
To everyone who said it is equal. I follow your math, but I can't help but see it physically.
Let's say the bottle (when full) holds 300 mL of liquid.
so after leaving 1/3 you have 100 mL of medicine left. (at full strength). He poors it up to 200 mL of what is now half strength medicine.
Why would adding 100 mL of 2x strength to the 200 mL of 1/2x strength bring it back to equilibrium?
I say it's weaker
For the last person before this entry:
your last line of why would adding 100ml of 2X strength to the 200ml of 1/2X strength bring it back to equilibrium...
initially you have 300ml of 1 x strength lets say this is 300(x).
now you have 200(x/2) + 100(2x) = 100(x) + 200(x) = 300(x)
In otherwords the same and you are an idiot for thinking that seeing it physically is better logic than simple algebra.
For those of you idiots who think that drinking 2/3 of a bottle of medicine will decrease its concentration by 2/3 you need to go back to school. This is directed to those beople who have calculations involving 1/6.
c=n/v this means that concentration = mol/volume
as the volume decreases so does the mol and therefore concentartion remains the same.
I think it would be the same.
Let say each 3rd is str lvl of 3 (str 9 in total).
So he drinks 2 3rds (str 6)leaving str 3.
He then fills up a 3rd with water, so its still str 3 but its now 2 3rds full.
He then fills it to the top (1 3rd) with 2xstr (str 6) bringing it back to a total of str 9.
M@
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