A solution that is 40% acid must be strengthened to become a solution

We need to make 40% acid solution into a 88% acid solution.

A1 = 40% Acid Solution
A2 = 100% Acid Solution (Pure Acid)
Final = 88% Acid Solution

A1:A2 = 1:4
If we have 10 ounces of A1, we need to have 40 ounces of A2.

Hence D

Thank you Karishma for the weighted average method.

let the pure acid to be added be x

initially, 10 ounce has 40% = 4 ounce acid and 60% = 6 ounce rest of the stuff
finally 10+x ounce has 88% acid and 12% = 0.12(10+x) ounce rest of the stuff

since rest of the stuff will remain equal in both cases, thereofore

0.12(10+x) = 6

or x = 40 ounce

Option D

let x=ounces of acid to be added
.4*10+x=.88(10+x)
x=40 ounces
D

Ballparking, 48 is impossible because the acidic will be more than 88%, a little lesser than 48, which is 40 Answer D.

I'd test the answer choices (possibly with a bit of estimation) on this one. The answer choices are easy numbers, while the math will require some algebra, so let's make it easier on ourselves.

Initially, we have 10 ounces of the solution, and .4(10) = 4 ounces of that consists of acid.

Start by testing (B): if we add 18 ounces of acid, we now have a total of 10+18 = 28 ounces of solution, and 4 + 18 = 22 ounces of that is acid.

How does 22/28 compare to 88%? It looks like we need an easy way to compare 88% to a bunch of different fractions, so let's convert 88% to a fraction as well: 88% = 88/100 = 22/25.

22/28 has a bigger denominator than 22/25, and the same numerator. Therefore, 22/28 is too small and we need to test a bigger answer choice.

Next, test (D): if we add 40 ounces of acid, we have a total of 10 + 40 = 50 ounces of solution, and 4 + 40 = 44 ounces of that is acid.

44/50 = 88/100 = 88%. The correct answer is (D).

chetan2u Bunuel

What do we mean by 10 ounces of 40% solution ??

I was assuming that 40% solution has 10 ounces

So 100% solution will have 25 ounces.

Total Solution has 25 ounces out of which acid is 40% and that again means 10 ounces of acid and remaining 15 ounces of water.

Now this 25 ounces has to be increased by adding acid such that the acid content is 88%.

(10+x)/(25+x)=88/100

On solving X comes out to be 100.

That means we need to add 100 ounces of acid .

Where am I wrong??

Hi,

10 ml of 40% solution...This means the solution is a mix of 40% of acid etc and 60% of water, and we are taking 10ml of it, so acid will be 4ml

Thank you chetan2u for a quick response. You mean to say that 40% solution and 10 ml means same thing??? Because it is already given that solution has 40% acid and 60% of water.

Initial quantity of acid=40% of 10=4 ounces
Final quantity of acid= 4+x(added acid)
Which is equal to 88% of( 10+added acid)
so (4+x)=0.88(10+x)
X=40 ounces
D:)

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.