A fruit juice blend consists of apple juice and sparkling water mixed in the proportion of 6 : 4. When 5 liters of sparkling water are poured into the blend, the ratio of apple juice to sparkling water changes to 6 : 5. How many liters of apple juice were present in the initial blend?

The correct answer is 30 L.

Step 1: Define variables using the initial ratio.
The initial ratio of apple juice to sparkling water in the blend is given as 6 : 4.
Let the common ratio factor be $x$.
This means:
Initial quantity of apple juice = $6x$ liters
Initial quantity of sparkling water = $4x$ liters

Step 2: Account for the added sparkling water.
When 5 liters of sparkling water are added to the blend:
The quantity of apple juice remains unchanged at $6x$ liters.
The new quantity of sparkling water becomes $4x+5$ liters.

Step 3: Formulate an equation using the new ratio.
The new ratio of apple juice to sparkling water is specified as 6 : 5. Expressing this as a fraction gives:

$\frac{6x}{4x+5}=\frac{6}{5}$

Step 4: Solve for $x$.
Cross-multiplying both sides of the equation:

$6x\times 5=6\times (4x+5)$

Divide both sides by 6:

$5x=4x+5$

Subtract $4x$ from both sides:

$5x-4x=5$

$x=5$

Step 5: Calculate the initial amount of apple juice.
Initial amount of apple juice = $6x$ liters.

Substitute $x=5$:

$\text{Apple juice}=6\times 5=30\text{L}$

Therefore, 30 liters of apple juice were present in the initial blend.