1. ## one of mixtures

Container A and Container B both contain a mixture of alcohol and water. The ratio of alcohol to water in container A is 1 to 3. The ratio of alcohol to water in container B is 1 to 9. 8 ounces of the mixture in container A is taken and mixed into container B. Then, 16 ounces of the mixture in container B is taken and mixed into container A. If both containers originally contained 40 ounces of mixture, what is the final ratio of alcohol to water in container A?

A. 1:7

B. 2:7

C. 5:19

D. 1:3

E. 10:27  Reply With Quote

2. ## Re: one of mixtures

C.
Container A has Alcohol:Water in 1:3 ratio. i.e. 1/4th alcohol out of 40oz
Thus orig alcohol in A, Aaorig = 10oz, orig water in A, Aworig = 30oz
Similarly, orig alcohol in B, Baorig = 4oz and Bworig = 36oz

Now 8oz of A is transferred to B, this contains 2oz of Alcohol and 6oz of water
Hence the new amount of alcohol in A is Aanew = 10-2 = 8oz, Awnew = 24oz
the new amounts in B are Banew = 4+2 = 6, and Bwnew = 42oz
The new concentration of alcohol in B is then 6oz in 48oz of solution

Now 16oz of B is transferred, this contains 6oz*16/48 = 2oz alcohol and 14oz water
The new value of Alcohol in A = Aanew + 2 = 10oz,new value of water in A = Awnew+14 = 38
Thus the ratio of alcohol to water in A is 10oz : 38oz or, 5:19
Hence C

Whew!  Reply With Quote

3. ## Re: one of mixtures

I got the same answer, C.

It took me about five minutes to solve though... I used the same approach as Greycellz. Is there a shorter way to solve this problem?  Reply With Quote

4. ## Re: one of mixtures

Agreed answer C. My question is how long did it take you guys to do this question? It took me about 4 solid minutes! Which is a lot if you get 3 questions like this in a row during your test!   Reply With Quote

5. ## Re: one of mixtures

i think the following approach might save time

A B
al wt ttl al wt ttl
org mix 10 30 40 4 36 40
8 ounce of A is 1/5th of A
stp1 -2 -6 32 +2 +6 48
16 ounce of B is 1/3rd of B 8 24 6 42
stp2 +2 +14 48 -2 -14 32
NET 10 38
10:38 = 5:19  Reply With Quote

6. ## Re: one of mixtures

the spacing got lost when I posted the solution above, the point is to make vertical columns, to save time  Reply With Quote

7. ## Re: one of mixtures Originally Posted by Bliss
I got the same answer, C.

It took me about five minutes to solve though... I used the same approach as Greycellz. Is there a shorter way to solve this problem?
Put it in the form of a table and just add and substract on each side
1-3 1-9
10-30 4-36
8- 24 6-42
etc.  Reply With Quote

8. ## Re: one of mixtures Hear me through here for a second - In A we have a ratio of 1 to 3 or 25% alchohol. We take 8 ounces of it, meaning 2 ounces of alcohol and put it in B. B was 1 to 9 or 10% alcohol so it's original 40 contained 4 ounces of alcohol. after the addition of A we have 48 total ounces with 4+2 = 6 ounces of alcohol. Take 16 ounces of this , which will contain 2 ounces of alchol and add it back to A, which was 32 with 8 and now will be 10 ounes of alcohol out of 48 total ounces. So in fractional terms we're at 5/19. Is this the same as the ratio though? it seems like it would be 5 parts alcohol to 14 parts water???? Where am i screwing this up?  Reply With Quote

9. ## Re: one of mixtures Originally Posted by jimmy slade Hear me through here for a second - In A we have a ratio of 1 to 3 or 25% alchohol. We take 8 ounces of it, meaning 2 ounces of alcohol and put it in B. B was 1 to 9 or 10% alcohol so it's original 40 contained 4 ounces of alcohol. after the addition of A we have 48 total ounces with 4+2 = 6 ounces of alcohol. Take 16 ounces of this , which will contain 2 ounces of alchol and add it back to A, which was 32 with 8 and now will be10 ounes of alcohol out of 48 total ounces. So in fractional terms we're at 5/19. Is this the same as the ratio though? it seems like it would be 5 parts alcohol to 14 parts water???? Where am i screwing this up?

10 ounes of alcohol out of 48 total ounces
Hence water = 48-10 = 38 ounces
Hence Ratio of A:W = 10:38 = 5:19  Reply With Quote

10. ## Re: one of mixtures

thank you, in my haste i said 10/48 = 5/19 not 5/24 which would be 5 to 19. duh. i like how this question makes you distinguish between ratios and fractions  Reply With Quote