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

If we add 10 oz of 100% solution, we will have a 60% mixture. Answer A out
If we add 20 oz of 100% solution, we will have an 80% mixture. Answer B out.

Further, we can use weighted average :

40---------------88------100

Distance between 88 and 40 is 48
Distance between 88 and 100 is 12

Ratio of 40% sol to 100% sol in the mixture is 12:48 or 1:4
So, the mixture will consist of 1 ratio unit of 40% sol and 4 ratio units of 100% sol. One ratio unit is 10, therefore 4 x 10 = 40.
Answer D

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

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.

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:)

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