A 5-Liter Jug Contains 4 Liters of a Saltwater Solution that is 15 GMAT Problem Solving

Question: A 5-liter jug contains 4 liters of a saltwater solution that is 15 percent salt. If 1.5 liters of the solution spills out of the jug, and the jug is then filled to capacity with water, approximately what percent of the resulting solution in the jug is salt?

1.  \(7\frac{1}{2}\)%
2.  \(9\frac{3}{8}\)%
3. \(10\frac{1}{2}\) %
4. 12 %
5. 15 %

Correct Answer: A

Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:

• A 5-liter jug contains 4 liters of a saltwater solution that is 15 percent salt.
• 1.5 liters of the solution spills out of the jug, and the jug is then filled to capacity with water.

Find out:

• The approximate percentage of the resulting solution in the jug is salt.

It's easy to answer the following equation and the arithmetic method can also be used in this situation. This can be explored in the following manner:
Let us just multiply the units in the question by 10 to solve the problem easily.

4L= 40
1.5L= 15
Original Mixture
The total solution is 40ml
The salt solution in it is 40 * 0.15 = 6ml
Water will come out to be 40 - 6 = 34ml

Now After the spill
Total water will be 40 - 15 = 25
Salt solution will be 6ml - (15 * 0.15) = 3.75ml

Now After the refill
The total water in the jug was 50ml
Salt will be 3.75 (unchanged)
3.75 / 50 = 7.5%

Therefore, \(7\frac{1}{2}\)% percent of the resulting solution in the jug is salt

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

• A 5-liter jug contains 4 liters of a saltwater solution that is 15 percent salt.
• 1.5 liters of the solution spills out of the jug, and the jug is then filled to capacity with water.

Find out:

• The approximate percentage of the resulting solution in the jug is salt.

Let's try the reasoning approach to solve this question-

It is mentioned that a 5-litre jug contains 4 litres of salt water solution with 15% of salt. This implies that it has 4000*.15 = 600 ml salt in it.
Now, 1.5 litres of the solution is spilled out, the remaining solution is 2.5 litres
Then the salt content will be 2500*.15 = 375ml.
Now, the jug is filled to full capacity with water i.e., now the jug has a 5 litre solution in it.
Therefore, the salt content is 375/5000 = 7.5%

\(7\frac{1}{2}\)% percent of the resulting solution in the jug is salt

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

• A 5-liter jug contains 4 liters of a saltwater solution that is 15 percent salt.
• 1.5 liters of the solution spills out of the jug, and the jug is then filled to capacity with water.

Find out:

• The approximate percentage of the resulting solution in the jug is salt.

The initial solution in the jug = 4 liters
The solution remaining after spill = 2.5 L
Water added to the remaining solution = 2.5 L water

Concentration of Salt in 2.5 L solution = 2.5 * 15/100 = 3/8
Concentration of Salt in total 5 L solution after adding water = 3/8 * 1/5 * 100 (Salt concentrate/ total solution x 100)
= 15/2 = 7.5%

\(7\frac{1}{2}\)% percent of the resulting solution in the jug is salt

“A 5-liter jug contains 4 liters of a saltwater solution that is 15”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The candidate needs to access information on the GMAT Problem Solving questions in order to solve numerical problems. The candidates can go through GMAT Quant practice papers to get familiar with varieties of questions that will help them to get better scores in the exam.

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