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Two different solutions of alcohol with respective proportio [#permalink]
13 Aug 2009, 15:12

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13% (04:22) wrong based on 2 sessions

Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4 times the amount of the second solution?

Re: Two different solutions of alcohol [#permalink]
13 Aug 2009, 15:19

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This post received KUDOS

tejal777 wrote:

Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4 times the amount of the second solution?

Detailed explanations please!

SOL: Lets assume that 40L of sol1 was mixed with 10L of sol2.

Alcohol in Sol1: 40*3/4 = 30L Alcohol in Sol2: 10*2/5 = 4L

Total Alcohol in the mixed solution of 50L = 30 + 4 = 34L

Alcohol concentration in the new sol: (34/50)*100 = 68%

Re: Two different solutions of alcohol [#permalink]
15 Aug 2009, 02:35

Good strategy by samrus. A slightly different way using variables:

Let sol1 have x liters, and sol2 have y liters. The ratio of alcohol to water in the final solution will be : [ (3/4)*x + (2/5)*y ] / [ (1/4)*x + (3/5)*y ]

Now, x=4y, substituting x in the above ratio, we get 17/8 as the ratio of alcohol to water in the final solution. Hence, concentration of alcohol is (17/25)*100 % = 68%

Re: Two different solutions of alcohol [#permalink]
16 Apr 2010, 16:36

A different approach: Alcohol in soln1 = 3/4 and in soln2 = 2/5 Using Alligation: 3/4--------?--2/5 4 : 1 So the resultant ratio (the ?) is at a 1/5th distance from 3/4 (or conversely at a 4/5th distance from 2/5. 3/4 - 2/5 = 7/20 Now, calculating 1/5th of 7/20 and subtracting it from 3/4 (3/4) - (1*5)/(7*20) = 75/100 - 7/100 = 68/100 = 68%

This approach is not quite advisable in this particular problem unless one is instinctive wrt alligation, but definitely awfully handy in other scenarios. This is just to enlighten people towards proper understanding of Alligation

_________________

In a Normal Distribution, only the Average'Stand Out'

Re: Two different solutions of alcohol [#permalink]
01 Jun 2014, 23:11

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