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There are two identical water jugs, A and B. Jug A is 3/7 full of water and Jug B is 8/11 full. What fraction of the capacity of a jug should water be poured out from jug B to jug A so that they both have the same amount of water?

Simple math, but not to me I tried many ways but to no avail (or i'm perhaps just dense).

The answer is 23/154

Please list down the steps and explain. Thank you!

Jasmine
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    Assume both jugs have capacity $77$ (chosen to avoid fractions). How much is in jug A? in jug B? How much needs to be transfered? What fraction of $77$ is that? – Gerry Myerson Apr 22 '15 at 09:58
  • @GerryMyerson. I was just typing the same ! Cheers. – Claude Leibovici Apr 22 '15 at 09:59
  • one of the approach: add the two given quantities, divide the result by 2, let this answer be X, (X - A) or (B - X) both will give you the required answer – Vikram Apr 22 '15 at 10:20

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Jug $B$ has $\frac{8}{11}-\frac37=\frac{23}{77}$ more water. Now take $\frac{23}{77}$ of water out of $B$ and pour in a jug $C$. Now both $A$ and $B$ have the same amount of water. Next pour half of $C$ in $B$ and the second half in $A$. This half is $\frac{23}{77}\times \frac12$.

Math-fun
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