There is a 120 Liter Mixture of Alcohol and Water GMAT Problem Solving

Question: There is a 120 liter mixture of alcohol and water. The ratio of alcohol to water is 7 : 5. A shopkeeper mixes a certain amount of water in order to make the ratio of alcohol to water as 5 : 6. Find the new quantity of water is what percentage of original quantity of water in the mixture?

1. 160%
2. 168%
3. 172%
4. 175%
5. 178%

“There is a 120 Liter Mixture of Alcohol and Water GMAT Problem Solving” - 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 amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

Given:

• Mixture of alcohol and water is 120 litres.
• The ratio of alcohol to water is 7 : 5.
• The shopkeeper mixes a certain amount of water in order to make the ratio of alcohol to water as 5 : 6

Find out:

• The new quantity of water is what percentage of original quantity of water in the mixture.

As per the problem statement, the mixture of alcohol and water is 120 litres.

The ratio of alcohol to water is 7:5.

So, we can easily say that 70 litres of alcohol and 50 litres of water are present in the solution.

Now, the shopkeeper changes the ratio of alcohol to water as 5:6. The shopkeeper mixes a certain amount of water to make this change in the ratio.

Here, 70 litres of alcohol is 5/11 part of the new solution

Then the quantity of new solution => 70*11/5 => 154 litres, which has 84 litres of water.

The new quantity of water percentage of the original quantity of water in the new mixture:

We need to calculate 84 litres of water is what percentage of 50 litres of the original solution.

84 = 50*x/100

X = 168

Correct Answer: B

Approach Solution 2:

Given:

• Mixture of alcohol and water is 120 litres.
• The ratio of alcohol to water is 7 : 5.
• The shopkeeper mixes a certain amount of water in order to make the ratio of alcohol to water as 5 : 6

Find out:

• The new quantity of water is what percentage of original quantity of water in the mixture.

As per the problem statement, the mixture of alcohol and water is 120 litres.

The ratio of alcohol to water is 7:5.

Now, the shopkeeper changes the ratio of alcohol to water as 5:6

Hence, we can bring the formula up as:

(7/5) (x) = 5/6

(7/5)(6/5) = x

x = 42/25

If we mulitply 42/25 by 4, we get 168/100

= 168%

Correct Answer: B

Approach Solution 3:

Given,

The ratio of initial Vinegar to Water = 7: 5

The ratio of new Vinegar to Water = 5: 6

Hence the equation forms:

The initial amount of vinegar = (7/12) × 120 = 70 L

The initial amount of water = (5/12) × 120 = 50 L

According to the question,
= 70/(50 + ×) = 5/6
= x = 84 - 50 = 34 L

Hence the required change in percentage = [(50 + 34)/50] × 100 = 168%
= The new quantity of water in the mixture = 168%.

Correct Answer: B

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