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December 23rd, 2016, 09:35 AM   #1
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alligation and ratio

The following problem seems somehow critical to me. The answer of the following question is 10.8 and 8.8.

Two liquids are mixed in the ratio 3:2 and the vendor gains 10% by selling the mixture at 11 USD (US Dollar) per liter. If the first liquid costs 2 USD more than the second, find the cost price of each of the liquids.

To solve this problem the ratio 3:2 was reversed into 2:3, and 2 USD was divided according to this ratio (2:3). In a lecture the solution of this problem was explained, but it explained this solution in such a way that only an expert will realize what lecturer of that video lecture was trying to say. Dividing USD 2 according to 2:3, 0.8 and 1.2 ware derived....and than in a complicated way this problem was solved. But the lecturer of that video lecture claimed that if anybody would follow the way he had showed will be able to solve this sort of problem within a couple of moments.

Please let me know why 3:2 was reversed into 2:3, and by which rule we can divide 2 USD into 0.8 and 1.2 according to the reversed ratio 2:3.
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December 24th, 2016, 06:22 AM   #2
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Let A and B be the amount, measured in liters, used of the two liquids. Since they are mixed in a ratio of 3:2, with the "3" referring to the amount of A used and the "2" referring to the amount of B used, 2A= 3B.

Perhaps that is what you mean by "the ratio 3:2 was reversed into 2:3". That is NOT a "ratio" of 2:3. A "ratio" is a fraction. A:B= 3:2 means $\displaystyle \frac{A}{B}= \frac{3}{2}$. From that, 2A= 3B.

Last edited by skipjack; December 24th, 2016 at 08:27 AM.
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December 25th, 2016, 07:14 PM   #3
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Please explain how 2A=3B can be used to divide 2? How USD 2 was divided or distributed according to 2:3 into 0.8 and 1.2? If we had been told we had total 2 USD, and in this amount the ratio of contributution of A and B is 2:3, only then we could divided USD 2 between A and B into 0.8 and 1.2. But here we have been told the first liquid costs 2 USD more than the second. Neither USD 2 is total amount, nor it is the total amount of liquids. Then in that video lecture cost price USD 10 was determined, and 0.8 and 1.2 were subtracted from 10 to determine the actual cost of A and B. The total procedure seems very awkward to me. Please don't suggest another method only to solve this problem. I would like to understand the method I have already described. Besides understanding the procedure the video lecturer had used, I may learn another methods to solve our problem. But first I need to understand the procedure we have been already described.

Thanks Country Boy for your help.

Last edited by Nousher Ahmed; December 25th, 2016 at 07:38 PM.
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December 26th, 2016, 08:44 AM   #4
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Can you please share the video?
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December 26th, 2016, 03:53 PM   #5
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https://m.youtube.com/watch?v=RmNKqp...le&hl=en&gl=US.
(The link of the video where I got the problem stated above).
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