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We are given 10 litres of juice mixture with juice:water=\(\frac{3}{2}\) i.e juice is 6 litre and water is 4 litre. It can also be said mixture has \(60\)% juice.

Now only 5 litres of this mixture is kept and pure 5 litre juice is mixed with it.
We can equate concentrations of juice before and after. i.e \(5*0.6 + 5*1 = 10*x\) { using volume of juice*concentration. 5 litre of old juice mixture*it had 60% concentration + 5 litre of new juice with 100% concentration = 10 litre of mixture* unknown concentration. }
x=0.8 i.e this mixture has 80% juice concentration.

Again 5 litre of this new mixture is mixed with 5 litre of pure juice. Again doing the same thing as above.
\(5*0.8+5*1=10*x\) We get x=0.9 , in 10 litre we have 90% juice then remaining 10% is water so juice:water = \(\frac{9}{1}\).

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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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