yellowho wrote:A six-liter solution is 85% alcohol. How many liters of pure alcohol must be added to produce a solution that is 90% alcohol?

How do you do this without having to take 85% of 6 or allegation?

Supposing x liters of pure alcohol must be added to the six-liter solution in order to produce a solution that is 90% alcohol, then

or 0.85 × 6 + x = 0.90 × (6 + x)

or 0.10 x = 6 × 0.05

or x = [spoiler]3[/spoiler] liters

It's interesting how you were able to solve this question with alligation method. We don't know the resulting solution's weight, neither we do know the starting concentration for the solution to be mixed with 85% of 6-liter solution. Alligation is a method to find the amount of two ingredients which are mixed together to form a new mixture with the given amounts or concentrations in the pre-mixed solutions.

One viable method to tackle this question is to take into account 85% alcohol concentration of 6-liter solution for producing another solution with the concentration 90% by adding pure alcohol --> 5.1 + a = 5.4 +0.9a, where a is denoted for alcohol, a=3 (the same as sanju proposed).

Otherwise we could also consider 10% concentration required of non-alcohol concentration in the new solution and apply this to the present non-alcohol concentration 0.9 (6*15%). We should find when 0.9 liters of solution becomes 10%. This will occur when we have solution 9 liters. Hence we need to increase our solution by 3 liters (9-6).

yellowho wrote:A six-liter solution is 85% alcohol. How many liters of pure alcohol must be added to produce a solution that is 90% alcohol?

How do you do this without having to take 85% of 6 or allegation?

you can absolutely do this with alligation. The mixtures are 85%, 100% and 90%. alligation is about weighted average. mixtures is just a subset of weighted average.

So I guess there's no getting around taking 85% of 6.

yellowho wrote:you can absolutely do this with alligation. The mixtures are 85%, 100% and 90%. alligation is about weighted average. mixtures is just a subset of weighted average.

So I guess there's no getting around taking 85% of 6.

Alligation would allow us to avoid having to take 85% of 6.

The proportion needed of each starting percentage is the positive difference between the other two percentages.

The proportion needed of the 85% solution = 100-90 = 10.
The proportion needed of the 100% solution = 90-85 = 5.
Ratio of 85% solution : 100% solution = 10:5 = 2:1.

Thus, the amount needed of the 100% solution is 1/2 the amount needed of the 85% solution:
1/2*6 = 3 liters.

Perhaps i didn't consider the pure alcohol solution as 100% concentration. Makes fine sense here
thanks

yellowho wrote:you can absolutely do this with alligation. The mixtures are 85%, 100% and 90%. alligation is about weighted average. mixtures is just a subset of weighted average.

So I guess there's no getting around taking 85% of 6.