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dev.gavande wrote:Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?
[a]1/5
1/4
[c]1/2
[d]3/4
[e]4/5
How to solve such questions?
Source: gmatclub tests
dev.gavande wrote:Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?
[a]1/5
1/4
[c]1/2
[d]3/4
[e]4/5
How to solve such questions?
Source: gmatclub tests
Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, a 45% solution of acid was obtained, what part of the original solution was replaced?
[a]1/5
1/4
[c]1/2
[d]3/4
[e]4/5
GMATGuruNY wrote:dev.gavande wrote:Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?
[a]1/5
1/4
[c]1/2
[d]3/4
[e]4/5
How to solve such questions?
Source: gmatclub tests
I received a PM asking me to comment.
Since the resulting percentage -- 40% -- is HALFWAY between 30% and 50%, EQUAL amounts of the 30% solution and the 50% solution are needed.
Thus, 1/2 of the 50% solution must be replaced with the 30% solution.
The correct answer is C.
If the resulting percentage were not halfway between 30 and 50, we could use ALLIGATION.
Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, a 45% solution of acid was obtained, what part of the original solution was replaced?
[a]1/5
1/4
[c]1/2
[d]3/4
[e]4/5
According to alligation:
The needed proportion of each percentage in the mixture is equal to the distance between the OTHER two percentages.
Proportion needed of the 30% solution = |45-50| = 5.
Proportion needed of the 50% solution = |45-30| = 15.
Ratio of 30% solution to 50% solution = 5:15 = 1:3.
1 part 30% solution is needed for every 3 parts 50% solution.
Thus, of every 4 parts:
1/4 will be from the 30% solution.
3/4 will be from the 50% solution.
Alligation uses the relative distances to determine HOW MUCH WEIGHT must be given to each percentage in the mixture.
Since 45 is closer to 50 than to 30, more weight must be given to the 50% solution.
Hence the resulting ratio, which gives 3/4 of the total weight to the 50% solution.
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