There are $2$ bottles, Bottle $A$ and Bottle $B$. Bottle $A$ has $5$ litres of a solution with $10 \%$ lime concentration. Bottle $B$ has $3$ litres of a solution with $20 \%$ lime concentration. An equal volume of lime solution was removed from each bottle and transferred into the other bottle.  After the transfer, the concentration of the lime solution became the same in both bottles. How much volume (in litres) of lime solution was transferred from each container? 
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