Problem Solving

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?

a) 5 : 3
b) 6 : 4
c) 8 : 2
d) 17: 3
e) 9 : 1

I am getting an answer of 9:1 (E)

Here's how.

C/W = 3/2 in a total of 10 lts of cocktail
3x + 2x = 10
x=2

So, currently 10 lts of cocktail will have 6 lts of C and 4 lts of W
Remove 5 lts and we now have 3 lts of C and 2 lts of W to which 5 more lts of C are added which would make the new cocktail have 8 lts of C and 2 lts of W.

Remove 5 lts of cocktail which would leave 4 lts of C and 1 lt of W. Add 5 more lts of C and it would have 9 lts of C and 1 of W.

So, the new ratio of C/W is 9:1

Can you please post the OA ?

You have 10 liters of mixture with a 3:2 ratio. That means 6l juice and 4l water. Removing 5l will give you 3l juice and 2l water. Adding 5l juice will give you a 8:2 ratio of juice and water. Removing 5l from this one gives you 4l juice and 1l water. Adding another 5l of juice you get 9l juice and 1l water, with a ratio of 9:1 juice to water.

OA - E