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A vessel contains milk and water in the ratio 3:2

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A vessel contains milk and water in the ratio 3:2 [#permalink] New post 26 Sep 2011, 09:49
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A vessel contains milk and water in the ratio 3:2. The volume of the contents is increased by 50% by adding water to this. From this solution 30 litre of the mixture is withdrawn and then replaced with water. The resultant ratio of milk to water in the final solution is 3:7. Find the original volume of the solution?

Also, please update how much time it took to resolve the problem. I want to check my level..whether it is really difficult and time consuming or not.
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Re: Ratio Proportion - tough problem 750+ [#permalink] New post 27 Sep 2011, 03:22
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jrymbei wrote:
Guys, Here's another problem I found while practicing today. Initially I was not able to figure out the problem itself and it took a long time to resolve this one..

A vessel contains milk and water in the ratio 3:2. The volume of the contents is increased by 50% by adding water to this. From this solution 30 litre of the mixture is withdrawn and then replaced with water. The resultant ratio of milk to water in the final solution is 3:7. Find the original volume of the solution?

Also, please update how much time it took to resolve the problem. I want to check my level..whether it is really difficult and time consuming or not.


The problem isn't very tough if your understand your mixtures well.
Work with each statement one by one.
Check out these post to understand the equations used:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... -mixtures/

Step 1:
"A vessel contains milk and water in the ratio 3:2. The volume of the contents is increased by 50% by adding water to this."

You have milk:water = 3:2
volume of this solution:volume of water added = 2:1 (Since volume is increased by 50%)
Let's focus on milk. Solution 1 with 3/5 milk is mixed with solution 2, which has no milk, in the ratio 2:1
Fraction of milk in final mixture of step 1 = [(3/5)*2 + 0*1]/(2+1) = 2/5
Say the volume of this final mixture is V litres.

Step 2:
"From this solution 30 litres of the mixture is withdrawn and then replaced with water. "

This just means that (V - 30) lt of our final mixture above is mixed with 30 lt of water.

Step 3:
"The resultant ratio of milk to water in the final solution is 3:7. "

This tells us that when we mix V-30 lt of mixture in which milk is 2/5 with 30 lt water, we get fraction of milk = 3/10

(V - 30)/30 = (0 - 3/10)/(3/10 - 2/5)
We get V = 120 lt

Since V was the volume of the final mixture in step 1, the volume of solution 1 in step 1 must have been 80 lt (because when you increase it by 50% i.e. 40 lt, you get 120 lt)

The original volume of the solution = 80 lt
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Re: Ratio Proportion - tough problem 750+ [#permalink] New post 27 Sep 2011, 09:30
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Hey - here's another approach, hope it helps.

Ratio of milk to water = 3:2...so we can take the volume of milk to be 3V and the volume of water to be 2V, and the total volume to be 3V + 2V = 5V.

Volume is increased by 50% by adding water. Therefore volume goes from 5V to 7.5V (an increase of 2.5V). Since only water has been added the NEW volume of water in solution is now 2V + 2.5V = 4.5V.

And the new ratio of milk to water is 3:4.5

Now 30 liters are withdrawn. Since we know the new ratio we can calculate that the volume of milk withdrawn is (30/7.5)*3 = 12 liters, which means 18 liters of water have been withdrawn (30 liters in total, minus 12 liters of milk).

Resultant volume of milk = 3V -12


Resultant volume of water = 2V + 2.5V -18 + 30
(Remember 30 liters of solution have been withdrawn, 18L milk and 12L water, and replaced with 30 liters of just water).

The ratio of these two will equal 3:7.

Solving: (3V-12)/(4.5V +12) = 3/7

V = 16 & the original volume is 5V = 5*16 = 80.

Please let me know what you think of this approach. Didn't take long at all.
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Re: Ratio Proportion - tough problem 750+ [#permalink] New post 27 Sep 2011, 13:51
I understood both the method by Ned and Karishma but the approach mentioned by Ned seems to more easy to interpret. Kudos to both of you for your help.

Just want to know is there any good guide where I can have better concept on mixtures where volume and concentrations are involved. I am having tough time to resolve this kind of problem.

Besides, do you think this kind of problems are for higher scoring, I mean is this problem is of good standard or we can expect more tougher then this one.
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Re: Ratio Proportion - tough problem 750+ [#permalink] New post 27 Sep 2011, 21:37
Expert's post
jrymbei wrote:
I understood both the method by Ned and Karishma but the approach mentioned by Ned seems to more easy to interpret. Kudos to both of you for your help.

Just want to know is there any good guide where I can have better concept on mixtures where volume and concentrations are involved. I am having tough time to resolve this kind of problem.

Besides, do you think this kind of problems are for higher scoring, I mean is this problem is of good standard or we can expect more tougher then this one.


This problem is definitely not very easy but it has been made tough by adding steps to it. Also, you need to re-trace the steps to get to 80 lts. That makes it a little time consuming and tedious. GMAT generally does not give you long tedious questions though they are tricky. The moment the trick clicks, you need 30 secs to solve the question. There is a fun element in the actual GMAT questions - they make you think hard, not calculate a lot.
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Re: Ratio Proportion - tough problem 750+ [#permalink] New post 28 Sep 2011, 03:44
I agree with you Karishma. Is there any guide for quick tricks. I had a long way to go to bring myself to a competent level.To me it's like a never ending story, I need real good score since my acad was not worth mentioning :cry: Lots of studies needs to be done.
Re: Ratio Proportion - tough problem 750+   [#permalink] 28 Sep 2011, 03:44
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