Alligation math with water problem

by Sheila
(Dunwoody, GA)

I am studying for the PTCB exam and came across this question.

How much water should be added to 95% ethanol to make 1L of a 30% solution?

I thought it was an alligation problem, but when I work through the problem I do not get the answer that goes with the question. I was thinking the 95% is the higher strength, 0% strength for the water, the desired quantity is 1000 ml and the desired strength is 30%. After the calculations I get 205 ml of water. The answer is suppose to 75 ml. Please show me the math. Thanks.

Reply (by Keith)

Hi Sheila, from the information provided in the question, it can definitely be solved using an Alligation tic-tac-toe grid. But, let's first take a step back for a moment and think about the question vs the answer provided.

If you took a 95% concentration and diluted it in half, in this case, that would be 500mL of each. That would give you (half of 95) a 47.5% solution, which is still too high, right, and even more water would be required. So right off the bat, you already know the answer's gotta be over 500mL.

If you're working that problem out of a book, don't be too shocked if the answer key is wrong. It is annoying, but all books seem to have a level of errors in their answer keys.

Anyhow, What I'm trying to convey about the half and half method I mentioned above is to use some techniques to shape up math questions before your pencil even touches the paper. Having a starting point will help you to get through the problem. Process of elimination will help you in many situations.

I suggest trying the problem over again using alligation to solve it.
I've put together some choices for you here to make it easier.

How much water should be added to 95% ethanol to make 1 L of a 30% solution?

A. 685mL of 95% + 316mL of SWFI

B. 600mL of 95% + 400mL of SWFI

C. 316mL of 95% + 685mL of SWFI

D. 590mL of 95% + 410mL of SWFI

Comments for
Alligation math with water problem

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Apr 18, 2011
This is a dilution problem
by: rhinson

Always think dilution problem when you see it's asking how much to add of a certain ingredient to determine strength/concentration of a set amount.

Also when you see the word "of" think of multiplication. In this case 1L "of" 30%

The formula for dilution problems is as follows.

(Q1)(S1) = (Q2)(S2)

Q1 = Original or starting quantity or volume
S1 = Strength - % concentration of original solution
Q2 - Final quantity or volume
S2 = Strength - % concentration of final or diluted solution

In this problem.
(X)(95) = (1000)(30)
95X = 30,000
X = 315.78 round to 316 ml of the 95% ethanol to make 1000ml of a 30% strength solution

Good Luck

Mar 25, 2011
que solution
by: Anonymous

30/100=x/1000 comes to 300 then 95/100=300/x comes to 316 so to check the qty of enthanol 1000-316 comes to 684 enthanol to finall check 316+684 1000mls(1letter).
the ans option a is wrong because when we add 685+316 comes to 1001mls there are 1000mLs in 1 liter not 1001.

Mar 25, 2011
by: Anonymous

I think it's a stock solution problem, not alligation. Try it and you will get the right answer.

Mar 23, 2011
by: B.M.


Mar 22, 2011
Alligation math with water problem
by: Sheila


Thank you for your timely response. The answer is C. Here is how I solved it:

Using the tic-tac-toe grid I calculated 30 parts of the 95% and 65 parts of the 0% then:

95/30 = 1000/x
Cross multiply and solve for x and I got 316. I then subtracted 316 from the 1000 and got 684.

By the way I stated the answer incorrectly. The answer showed 685ml. I found this question on the Quizlet site. Are their answers always correct?


- Hi Sheila, I've not ever been to that site. If it's online, it's likely accurate. Websites can be fixed, whereas printed books are permanent. Glad you got the problem figured out. Confidence builds when you struggle with these things and then figure them out. Thanks for using the site. -Keith

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