A solution of salt and water has a volume of 1 Gallon. The solution is...
Steps 1 & 2: Understand Question and Draw Inferences
In the initial solution, let the amount of Salt be x Gallon
So, the amount of Water will be (1-x) Gallon
As a result of heating this solution on the flame, some water evaporates.
Let the volume of evaporated water be y Gallon
So, the amount of water left = (1 – x – y) Gallons
The amount of salt is still x Gallons.
Total volume of the solution left = (1-y ) Gallons
So, the percentage of salt by volume in the final solution =
Thus, in order to find the percentage of salt by volume in the final solution, we need to know the value of x and y.
Step 3: Analyze Statement 1
As per Statement (1),
The initial solution contained 10% salt by volume.
=> x = 10% of 1 Gallon
From this equation, we will be able to find the value of x. But we get no clue about the value of y.
Therefore,
Statement (1) is not sufficient.
Step 4: Analyze Statement 2
As per Statement (2),
The volume of the final solution is ¾ Gallon.
=> 1 -y = 3/4
=> y = 1/4 Gallon
Thus, Statement (2) gives us the value of y. But we have no clue about the value of x.
Therefore,
Statement (2) is not sufficient.
Step 5: Analyze Both Statements Together (if needed)
From Statement (1),
From Statement (2),
y = 1/4
Now that we have the values of both x and y, from Equation 1, we will be able to find the percentage of salt by volume in the final solution
Thus, both statements taken together are sufficient to arrive at a unique solution.
Answer: Option (C)