A Mixture of 70 Litres of Alcohol and Water Contains 10% of Water GMAT Problem Solving

Question: A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture?

1. 1 litre
2. 1.5 litre
3. 2 litres
4. 2.5 litres
5. 3 litres

Correct Answer: C
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:

• A mixture of 70 litres of alcohol and water contains 10% of water.

Find out:

• The amount of water added to the mixture to make the water 12.5% of the resulting mixture.

The initial mixture of a total of 70 litres holds 10% water
Therefore, we can say:
The initial mixture has 7 litres of water and 63 litres of alcohol.
Only water is added to the mixture and the concentration of water becomes 12.5%.
The fractional equivalent of 12.5% = 1/8
Let x litres of water be added to the mixture.
Therefore, the concentration of water = (7 + x) litres
The concentration of the mixture becomes = (70 + x) litres.
Since 12.5% or 1/8 of the total mixture is water, then (7 + x) (70 + x)= \(\frac{(7+x)}{(70-x)}=\frac{1}{8}\)
=> 8(7 + x) = 70 + x
=> 56 + 8x = 70 + x
=> 7x = 14
Therefore, x = 2.
Hence, the amount of water added to the mixture = 2 litres.

Approach Solution 2:
The problem statement states that:
Given:

• A mixture of 70 litres of alcohol and water contains 10% of water.

Find out:

• The amount of water added to the mixture to make the water 12.5% of the resulting mixture.

Initial Alcohol percentage = 90% = 0.9 * 70 = 63 litres
Initial Water percentage = 10% = 0.1 * 70 = 7 litres
New Alcohol percentage = 87.5% = 63 litres .
1% percentage =\(\frac{63}{87.5}\)= 0.72 litres
New water percentage = 12.5% = 0.72 * 12.5 = 9 litres
The amount of water to be added = 9 - 7 = 2 litres.

Approach Solution 3:
The problem statement implies that:
Given:

• A mixture of 70 litres of alcohol and water contains 10% of water.

Find out:

• The amount of water added to the mixture to make the water 12.5% of the resulting mixture.

The quantity of alcohol should not change.
The total quantity of the given mixture is = 70 litres.
In the given mixture, the 10% water equals 7 litres of water.
In the given mixture, 90% alcohol equals 63 litres of alcohol.
After adding water, the new mixture will hold 12.5% water.
This indicates 1/8 water and 7/8th part of the mixture will be alcohol.
Since the alcohol quantity will remain the same, then we can say:
7/8th of the Volume of the new mixture = 63.
Volume of new mixture = 63 * (8/7) = 9 * 8 = 72 litres.
Initial volume = 70 litres. New volume = 72 litres.
Therefore, the amount of water added = 2 litres.

“A mixture of 70 litres of alcohol and water contains 10% of water”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide 2021”. The candidates must possess concrete knowledge of mathematics in order to solve GMAT Problem Solving questions. The candidates can follow GMAT Quant practice papers to get familiar with different types of questions that will improve their mathematical knowledge.

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