A full bottle contains 40% oil, 20% vinegar, and 40% water. The bottle

Question

A full bottle contains 40% oil, 20% vinegar, and 40% water. The bottle is poured into a larger bottle, four times as big as original. The remaining space in the larger bottle is then filled with water. If there was 8 ml of oil in the original bottle, how much of water is in the final mixture?

Ans: 68 mL.

Ans:  68 mL .

folks - can you please let me know how to approach these mixture problems as I think this is my weakest area. I struggle to approach such questions and gets all mixed up. So can someone please explain me the step-by-step approach and the concept of doing these questions? I get confused between percents and numbers.

For example the only thing I can calculate in this questions is the amount of oil by doing: Lets say there was x amount of oil in the original bottle. So 40/100 x=8, then x = 8. what to do after next is not coming into my mind. So your help will be very much appreciated.

sudhir18n · Answer

I think the easiest way to do this is..
the question tells that there was 8 ml of oil in the original bottle = 20% 
hence total = 20 ml ( 8 ml oil , 8 ml water and 4 ml vinegar)

larger bottle is 4 times the older one = 4* 20 =80
now this 80 includes 60 ml of water + 20 ml of solution that we pour from the old bottle
hence total water

60 + 8 = 68 ml

enigma123 · Answer

Thanks Sudhir. Good explanation buddy. Sorry to be pain but can this be solved by taking variables?

sudhir18n · Answer

Even if you take variables you will reach the solution the same way as I did it.
Assume the solution in old bottle = X
now we know 40% is oil = 40% of X 
The question tells us that oil in the old bottle was 8 ml
40% of X = 8 ml 
solve for X ; X = 20

jamifahad · Answer

Let the total volume of original bottle be x
Then question says 40% of x is oil.
Also question mentions that there is 8ml of oil in original bottle.
Set up equation--> 40% of x = 8
40 * x /100 = 8
x=20.
Hence oil in original container is = 8mL (40 % of total volume)
vinegar in original container is = 4mL (20 % of total volume)
water in original container is = 8mL. (40 % of total volume)

Now we take a container which has 4 times volume of original container. 
So, volume of new container = 4*20=80
In this new container we pour oil, vinegar and water from original container. 
Volume occupied in new container by oil, vinegar and water from original container = 8+4+8=20mL
Hence volume left in new container = 80 - 20 = 60mL

As per question, remaining space in the larger bottle is then filled with water. i.e 60mL is filled with water.
Hence total water in new container = 60mL + 8mL(this one poured from old container)
=68mL

Check below link for more info

https://gmatclub.com/forum/mixture-gmat-questions-mixtures-ratios-master-list-79529.html

A full bottle contains 40% oil, 20% vinegar, and 40% water. The bottle

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