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by dev.gavande » Tue Oct 04, 2011 1:54 am
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
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by Anurag@Gurome » Tue Oct 04, 2011 2:11 am
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


Let the total part = 1 and x part is replaced from it.
Then (1 - x) * 50 + 30x = 40 * 1
50 - 50x + 30x = 40
10 = 20x
x = 1/2

The correct answer is C.
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by sl750 » Tue Oct 04, 2011 2:13 am
There are many ways to solve this problem

This can be seen as a weighted avg problem. Notice here that 40% is exactly half way between 30% and 50%.

We have equal amounts of 50% solution and 30% solution. Let that amount be x

(x*50%+x*30%)/2x = 40%. So the ratio here is 1:1 or 1/2
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by GMATGuruNY » Tue Oct 04, 2011 8:33 am
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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by GmatKiss » Tue Oct 04, 2011 11:36 am
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.


Hi Mitch,

Thanks for the comment and the concept of Alligation!
You mean a lot to the forum :)
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