Bunuel wrote:
A solution of salt and water is 10 percent salt by weight. After a period of time under pressure and heat, a portion of the water evaporates so that the solution is 40 percent salt by weight. What is the ratio of the initial weight of water to the final weight of water in the solution?
(A) 1 to 6
(B) 1 to 4
(C) 1 to 3
(D) 4 to 1
(E) 6 to 1
There are multiple ways of solving this.
Method 1: Ratios approachInitially there was 10% salt i.e. 10 parts salt for 90 parts water. Some water evaporated and we are left with
x parts water. The ratio of salt to water became 40:60 then i.e. 2/3
\(\frac{10}{x} = \frac{2}{3}\)
So x = 15
Hence 90 parts water became 15 parts water i.e. a ratio of 6 to 1.
Check this video for a
discussion on Ratios.
Method 2: MixturesWe can use mixtures concepts not just when two solutions are added but also when one solution is separated. (10% salt solution separated into 'pure water' and '40% salt solution')
\(\frac{w1}{w2} = \frac{(A2 - Aavg)}{(Aavg - A1)} = \frac{(40 - 10)}{(10 - 0)} = \frac{3}{1}\)
Total 10% solution was 4 parts of which 1 part is 40% solution and 3 parts is water. So 100 ml of 10% solution split into 25 ml of 40% solution (which will have 15 ml of water) and 75 ml of pure water.
Required ratio = 6 to 1
Answer (E)
Check this video for a discussion on
weighted averages and this video for
mixtures.Alternatively, check out this blog post for a discussion on
weighted averages and this for
mixtures.