Five gallons of a solution of vinegar and water with 8% vinegar is to

Its been given that there is 5 gallons of water and Vinegar with 8% of vinegar.
ie 8% of vinegar in 5 gallons is (8/100)*5 = 0.4 gallons of Vinegar and 4.6 gallons of water.

To make it 4% how many gallons of water should be added to the existing solution(5 g)

let us say it is x. i.e current Vinegar solution/(current soln in gallons + water to be added)=0.04
>> 0.4/(5+x)=4%

0.4/(5+x)=0.04 >> 5+x= 0.4/0.04=10

>>x=5

Ans B

Hi rvc27,

In these types of mixture questions, if the answers are numbers, then it's likely that you can TEST THE ANSWERS to quickly get to the solution. Here's how:

First, we need to know about the original mixture of vinegar and water. We're told that a 5 gallon mixture is 8% vinegar....

(5 gallons)(.08) = 0.4 gallons vinegar
The rest = 4.6 gallons water

We're told to ADD WATER until the mixture goes from 8% vinegar to 4% vinegar.

Since the answer choices are numbers, we know that one of them will lead us to a 4% mix when added to the current mix. Changing 8% to 4% means that we have to add a significant amount of water (relative to what we started with), so I would TEST one of the bigger numbers first.

Let's TEST B

If 5 gallons of water were added, then we'd have....
0.4 gallons vinegar
9.6 gallons of water

0.4/10 = 4% vinegar. This is EXACTLY what we're looking for, so B MUST be the answer.

Final Answer:

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

May I propose another approach here? That, because coming from a psychology background and pretty much learning math through my gmat practice, the more mathematical approaches are still sometimes difficult for me.

So, as we said above, we have 5 gallons of solution, with 0.4 gallons of vinegar (8% of solution) and 4.6 gallons of water (92% of solution). Now, we can say that if the vinegar is the new solution is 4% of the total solution, then water must be 98%.

Then, we can say: 4.6 gallons of water is 92% of the solution - x gallons are 98%? Or..

4.6 ---> 92
x ---> 98

92x=4.6*98
92x=450.8
x=450.8/92
x= 4.9, so rounding up to 5.

Initial .................. Vinegar .................... Water ............... Total

8% Vinegar ............ \(\frac{40}{100}\) ........................ \(\frac{460}{100}\) .............. 5

"x" water added .... \(\frac{40}{100}\) ....................... \(\frac{460}{100} + x\) ......... 5+x

Given that post addition of water, vinegar concentration should decrease to 4%

\(\frac{4}{100} (5+x) = \frac{40}{100}\)

x = 5

Answer = B

Yes, the question can be very easily solved by considering it a mixture problem where 8% vinegar solution is mixed with 0% vinegar solution (pure water) to make a 4% vinegar solution.


w1/w2 = (A2 - Aavg)/(Aavg - A1) = (0 - 4)/(4 - 8) = 1/1
So weights of both solutions should be same. We should put 5 gallons of water in 5 gallons of 8% vinegar solution.
Answer (B)
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let w=gallons of water to be added
.08*5=.04(5+w)
w=5 gallons
B

Let x = amount of water to be added
A = solution with 8% vinegar
B = water, which 0.0 percent vinegar

(% A)(Vol A) + (% B)(Vol B) = (% of A+B)(Vol A+B)

You do not need the 0x on LHS. It's a reminder that water IS being added, but that its concentration /percent vinegar has no weight.

\(.08(5) + 0.0(x) = .04(5 + x)\)
\(.40 + 0x = .20 + .04x\)
\(.20 = .04x\)
\(x = \frac{.20}{.04}=\frac{20}{5}=5\)

Answer B
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Initial vinegar content = 8%

Final vinegar content = 4%

Vinegar content in the additional water that is added = 0% (the water is 100% water and 0% vinegar)

Thus the ratio of the initial mixture and water that is added = (4-0) : (8 - 4) = 1 : 1

Thus in the 5 gallons of initial mixture, you will have to add another 5 gallons of water to get a 4% vinegar in the final mixture.

Correct answer is Option B.

Note: The method that is used here is Alligation, which is similar to weighted averages, but faster to calculate.


Regards,
Saquib
e-GMAT
Quant Expert
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