Malegria Posted March 4, 2005 Share Posted March 4, 2005 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 Quote Link to comment Share on other sites More sharing options...
greycellz Posted March 4, 2005 Share Posted March 4, 2005 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! Quote Link to comment Share on other sites More sharing options...
Bliss Posted March 4, 2005 Share Posted March 4, 2005 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? Quote Link to comment Share on other sites More sharing options...
800needed Posted March 4, 2005 Share Posted March 4, 2005 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!:hmm: Quote Link to comment Share on other sites More sharing options...
prep2max Posted March 4, 2005 Share Posted March 4, 2005 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 Quote Link to comment Share on other sites More sharing options...
prep2max Posted March 4, 2005 Share Posted March 4, 2005 the spacing got lost when I posted the solution above, the point is to make vertical columns, to save time Quote Link to comment Share on other sites More sharing options...
soussou Posted March 4, 2005 Share Posted March 4, 2005 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. Quote Link to comment Share on other sites More sharing options...
jimmy slade Posted March 4, 2005 Share Posted March 4, 2005 :mad: 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? Quote Link to comment Share on other sites More sharing options...
comp_bos Posted March 4, 2005 Share Posted March 4, 2005 :mad: 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? 10 ounes of alcohol out of 48 total ounces Hence water = 48-10 = 38 ounces Hence Ratio of A:W = 10:38 = 5:19 Quote Link to comment Share on other sites More sharing options...
jimmy slade Posted March 4, 2005 Share Posted March 4, 2005 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 Quote Link to comment Share on other sites More sharing options...
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