A filled vessel contains 5 parts of water and 7 parts of syrup. How mu

Question

A filled vessel contains 5 parts of water and 7 parts of syrup. How much of the mixture must be drawn out and replaced with water, so that the mixture has 50% water and 50% syrup ?

(A) 1/7
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2

GMATinsight · Accepted Answer

Let, Total Quantity = 5+7 = 12 parts i.e. Water = 5 and Syrup = 7 parts

x part is replaced with water

Syrup in x  = (\frac{7}{7+5})*x = (\frac{7}{12})*x

After replacing x parts by water, Syrup in Mixture  = 7 - (\frac{7}{12})*x

Remaining Syrup  = \frac{50}{100}*12 = 6

i.e.  7 - (\frac{7}{12})*x = 6

i.e.  x = \frac{12}{7}

i.e. Replaced quantity  = \frac{12}{7}/12 = \frac{1}{7}

Answer: Option A

stne · Answer

GMATinsight ,

Isn't the question asking for x i.e. how much has been taken out and replaced with water ie. x= 12/7 has been taken out and replaced.

Cannot get the logic of dividing of 12.

Can you explain?

Thank you.

GMATinsight · Answer

stne

The question is about finding  the fraction of solution replaced to get desired outcome

We have assumed that if there are 12 parts then e will have to replace  \frac{12}{7}  parts out of them.

i.e. Required fraction = Replaced Quantity/Total Quantity = (12/7)/12 = 1/7

I hope this help!

stne · Answer

GMATinsight , sorry sir, Even though the word " fraction" is not specifically mentioned in the question, what phrase/ sentence implies that we are looking for a fraction.

Thank you.

GMATinsight · Answer

stne

The question doesn't offer quantities of teh solution. 5 parts and 7 parts are only the representing teh ratio of different parts of mixture.

When in a question that doesn't offer exact quantities of parts in mixture, question prompts   "How much should be replaced....."   then the answer is always expected and calculated in fractions (unless mentioned that answers are required in percentages).

hr1212 · Answer

Let the initial quantity of mixture be T, then the quantity of water will be 5T/12.

Let x be the quantity of mixture replaced, in other words x will also be the quantity of water added and T/2 is the required quantity of water in the final solution.

Quantity of water in initial solution (after x units are removed) + Quantity of water added (x units added) = Quantity of water in final solution

So, (T-x)(5/12) + x = T/2

Solving this gives us, x = T/7, which means 1/7 of the initial quantity of mixture needs to be replaced with water to get the desired solution.

Answer: A

Kinshook · Answer

A filled vessel contains 5 parts of water and 7 parts of syrup.

How much of the mixture must be drawn out and replaced with water, so that the mixture has 50% water and 50% syrup ?

Let the the mixture that must be drawn out be x.

Before: - 
Syrup = 7/12
Water = 5/12
Total = 1

After: - 
Syrup = 7/12(1-x)
Water = 5/12 + 7x/12
Total = 1

7/12 - 7x/12 = 5/12 + 7x/12
2/12 = 14x/12
x = 1/7

IMO A

djangobackend · Answer

using weighted avgs. say total amount = 24 
now lets deal with water only - 
w/s = 5/7 so percent water = 5/12* 100 = 125/3 
now, final conc. of water = 50 and we are adding x litres (this is replaced amount) of 100% water 
so using weighted avg. equation we get - 
24 (50- 125/3) = 50*x
which gives x= 4 
so total amount will be 24+4 = 28 
so replaced amount = 4/28 = 1/7

PSKhore · Answer

Why are we not taking out the water and then add the syrup to the water?
I can see that you've only added the syrup to the water

Bunuel · Answer

That's a misunderstanding. The mixture is removed in the same ratio of water to syrup (5:7), so when x is removed, both water and syrup are taken out.

Then, the entire x is replaced with water only, not syrup.

So:

Water becomes: 5/12 - 5x/12 + x = 5/12 + 7x/12 
 Syrup becomes: 7/12 - 7x/12

We're not adding syrup. We're removing part of both and replacing the whole x with water only.

18. Mixture Problems

Theory

Weighted Average and Mixture Problems on the GMAT  
  Tips and Tricks: Mixtures

Questions

DS Questions  
  PS Questions

For more check  Ultimate GMAT Quantitative Megathread

PSKhore · Answer

Oops I didn't realise x-5x/12 would lead to 7x/12... Breaking it down this way is easier to understand, thank you!

Water becomes: 5/12 - 5x/12 + x = 5/12 + 7x/12    
    Syrup becomes: 7/12 - 7x/12

A filled vessel contains 5 parts of water and 7 parts of syrup. How mu

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GMAT Problem Solving (PS) Questions

A filled vessel contains 5 parts of water and 7 parts of syrup. How mu

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