More A in B or more B in A?

[Charles]

You have two containers. Container A has one gallon of liquid A in it. Container B has one gallon of liquid B in it. You take a cup of A and pour it into the B container and mix it. Then you take a cup of the mix in the B container and pour it into the A container.

Is there more liquid A in the B container or more liquid B in the A container?

[IFF]

my calculation is giving me an equal amount of A in container B as to B in container A.

Being european, I worked on litres rather than gallons.
I said 1 litre in both.
My cup size is 200ml (assuming it's the same cup so therefore each cup holds the same amount of liquid) so after the first swap, container A has 800ml of liquid A and container B has 1,000 ml of liquid A and 200 ml of liquid A.
Using the same cup and assuming i have properly mixed it and I spilled none, extremely unrealistic , when it comes to putting the mixture, i take 200 ml and in the proportion of 1/6ths A and 5/6ths B being (200/1200 and 1000/1200), this would be 33 ml of A (200 * 1 /6 ) and 167 ml of B (200 * 5/ 6) so conclusion after this: you have 833 ml of liquid A in container A and 167 ml of liquid B in container A and you have 833ml of liquid B in container B and 167 ml of liquid A.

there is no way that either container would have more of either liquid in it as with the same cup size's you have transported the same amount of liquid each time so there has to be an inverse amount in the opposite container.


of course things would be different if you took 20% from container A and then 20% from container B. In this scenario, there would be more B in container A (200ml of B in A while 160ml of A in B) but given that cup size doesn't change, this doesn't happen.

ok, charles, where did i go wrong?

[Ratbag]

ummm didn't we do this one already?

[Charles]

my calculation is giving me an equal amount of A in container B as to B in container A.

You be is correct.