A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 40% lemonade syrup?

A. 1.5
B. 1.75
C. 2.14
D. 2.34
E. 2.64

Let the total solution is 150 L with 80 L water & 70 L syrup.

To make 40% syrup solution, the result solution must have 90 L syrup and 60 L syrup.

Therefore we are taking 10 L of syrup from initial solution and replacing with water.

using urinary method:
70 L syrup in 150 L solution
10 L syrup in 21.4 L solution

We started by multiplying 10
Now to get to the result we need to divide by 10 => amount of solution to be replaced with water = (21.4/10) = 2.14.

Correct option : C

C it is
total solution 15, Lemonoid = 7
we want to make it 40% lemonoid >> so 6 parts of lemonoid
so we need to remove 1 part of lemonoid
each part of solution has 7/15 lemonoid
that means for 1 part lemonoid will be in 15/7 = 2.14 prt of solution which will be replaced with water

Yep. When I read the question, I thought that either the question is worded improperly or the word 'water' after '8 parts' is missing. But I figured that if it is 8 parts solution then the options don't match the answer so it must be 8 parts water. Don't fret!
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8/7 is not the new ratio. Again: we want to remove 1 liter of syrup, but with every 1 liter of syrup comes 8/7 liters of water (because if s=1 then w from w/s=8/7 becomes 8/7), hence in order to remove 1 liter of syrup we should remove total of 1+8/7 liters of mixture.

Hope it's clear.
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1. Let the number of parts of the original solution be 30.
2.The original solution contains 14 parts lemonade and 16 parts water
3. The new solution contains 12 parts lemonade and 18 parts water
4. Let x parts of solution be replaced. Water replaced is 16x/30
5. x parts of water is added
6. From (2) and (3) we see the net increase in water is 18-16=2 parts
7. From (4) and (5) we see the net increase in water is x-(16x/30) parts
8. Equating (6) and (7) we have x=4.28
9. If we take the total number of parts as 30, the solution removed is 4.28 parts. Therefore for a total of 15 parts, the solution removed is 2.14 parts
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My solution with explanation:

Def took longer to rationalize than I would have allowed on test day...anyway, here's my take:

Replacing one part of the solution with water will take away 8/15 of water and 7/15 of Lemonade (and replace it with 15/15 water)...essentially just switching out 7/15 of Lemonade with 7/15 Water for every part removed...

So, from a Lemonade composition perspective:

[7 - (7x/15)]/15 = 4/10

x=15/7
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Hi VSabc,

This question is a little tougher than a typical "mixture" question. The prompt tells us to REPLACE some of the existing mixture with pure water (with the goal of turning the new mixture into a 40% syrup mix.

To start, we have 15 total liters -->a mixture that is 8 liters water and 7 liters syrup.

If we pour 1 liter of this mixture into a glass, we would have a liquid that is 7/15 syrup (so a little less than half syrup).

For the mixture to be 15 total liters and 40% syrup, we need the mixture to be 9 liters water and 6 liters syrup.

In basic math terms, we need to pour out enough of the mixture that we remove 1 full liter of syrup; when we pour an equivalent amount of water back in, we'll have 15 total liters (and 6 of them will be syrup). Since each liter is 7/15 syrup......

We need to remove 15/7 liters and replace them with 15/7 liters of pure water.

15/7 is a little more than 2 liters (about 2.14 liters)

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Hi Karishma,

Thanks for explaining it so well. I got it wrong as I thought we have to give answer in terms of lemonade.
So, here can we say that replacing 1 unit of lemonade and 1.14 units of water will serve the purpose ?

Regards,

Gaurav