GMAT Problem Solving - How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%?

Question: How much pure alcohol should be added to 400 ml of a 15% solution to make the strength of the solution 32%?

1. 80ml
2. 100 ml
3. 120 ml
4. 150 ml
5. 160 ml

‘How much pure alcohol should be added to 400 ml of a 15% solution to make the strength of the solution 32%?’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review".
To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:
Given in the question that we have 400 ml of a 15% solution. It is asked to find out the amount of alcohol to be added to the solution to make its strength 32%.
Firstly the amount of alcohol in 400ml of solution = 15%
Amount in ml = 400 * 15%
= 400 * 15/100
= 4*15 = 60ml
There is 60ml alcohol in the 400 ml solution.
Amount of water = total volume - amount of alcohol
= 400 - 60 = 340ml
When we will increase the strength of the solution by adding more alcohol to the solution the volume of water will not change.
Also when there is 32% concentration of alcohol then it will contain 100 - 32 = 68% of water.
As the volume of water will not change before and after concentration,
Let the total volume after adding more alcohol be x
340 = 68% of x
340 = (68 / 100) * x
X = 340 * 100 / 68
X = 500 ml
The amount of alcohol added will be 500ml - 400 ml = 100 ml
Therefore option B will be the correct answer.

Correct Answer: B

Approach Solution 2:
Given in the question that we have 400 ml of a 15% solution. It is asked to find out the amount of alcohol to be added to the solution to make its strength 32%.
Firstly the amount of alcohol in 400ml of solution = 15%
Amount in ml = 400 * 15%
= 400 * 15/100
= 4*15 = 60ml
There is 60ml alcohol in the 400 ml solution
Now let y ml of alcohol be added to the solution to increase its strength = 32%
Percentage of alcohol in the solution = 32
(60 + y)/ (400 +y) = 32 / 100
100 (60 + y) = 32 (400 + y )
6000 + 100y = 12800 + 32y
68y = 6800
Y = 6800/68 = 100
We get y = 100ml
Therefore 100ml of alcohol was added to make the solution strength 32%.
Option B is the correct answer.

Correct Answer: B

Approach Solution 3:

Given in the question that we have the amount of alcohol in 400ml solution of 15% strength

=400×15​/100ml=60ml

Let the required amount of alcohol be added =x ml.

It will increase the amount of the solution by x ml.

Therefore, the amount of alcohol now =(60+x)ml

and the amount of the solution=(400+x)ml.

Then, the strength =32%=(400+x)/(60+x)​=32​/100

This implies 25x+1500=3200+8x

this implies 17x=1700

hence the value of x=100.

So, the required amount of pure alcohol to be added is 100ml.

Correct Answer: B

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