* mixture prob.what did i miss?

[tejal777]

A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?
1. 5 : 3
2. 6 : 4
3. 8 : 2
4. 17 : 3
5. 9 : 1

My solution:
Original mixture has CJ:6 lts and water 4 lts.
step 1:
5 lts are removed.Therefore,
CJ remaining: 6 - {3/5 x 5} = 3lts.
Water remaining: 4 - {2/5 x 5}=2lts.
now 5 lts of CJ are added bringing the mixture to CJ:8 lts and water:2 lts.

step 2:
5 more lts are removed.
amount of CJ removed: 8 x 3/5 = 4.8 lts
amount of wtr removed:8 x 2/5= 0.2lts.
5 lts of CJ added Resulting in CJ: 8.20lts and 1.80 lts of water.

where did i mess up???

[vsudheerk]

You made two mistakes:
1. Ratio of CJ/W changes after 1st operation. Use updated ratio for calculations in step2.
2. Remaining amount calculation in step2 is wrong. Do it like in step 1 but use correct updated CJ/W ratio as mentioned above.

[JonathanSchneider]

Please post the source, otherwise we must delete!