A tank contains 149.99 liters of juice and soda, in which 49.99 liters are soda. If 30.12 liters of mixture are taken out and 10.02 liters of pure juice are added, then find the ratio of juice to soda in the resultant mixture.

The correct answer/option is 9:4 (Option 5).

Step 1: Determine the initial quantities of juice and soda in the mixture.
The total volume of the mixture in the tank is 149.99 liters.
The volume of soda in this mixture is 49.99 liters.
Therefore, the volume of juice in the mixture is:
Juice = Total mixture - Soda
Juice = 149.99 - 49.99 = 100.00 liters.

Step 2: Find the ratio of juice and soda in the initial mixture.
The ratio of juice to soda is:
Juice : Soda = 100.00 : 49.99
Approximating these quantities to the nearest integer for simplicity of calculation (since the values are extremely close to integers, i.e., 149.99 ≈ 150 liters, 49.99 ≈ 50 liters, and 100.00 = 100 liters):
Total volume ≈ 150 liters
Soda ≈ 50 liters
Juice ≈ 100 liters
Ratio of juice to soda = 100 : 50 = 2 : 1.

Step 3: Calculate the quantities of juice and soda removed.
When 30.12 liters (which is approximately 30 liters) of the mixture is taken out, it is removed in the same ratio of 2 : 1.
Using the approximated values:
Total volume of mixture removed ≈ 30 liters
Soda removed = 30 × (1 / 3) = 10 liters
Juice removed = 30 × (2 / 3) = 20 liters.

Step 4: Find the remaining quantities of juice and soda.
Remaining juice = 100 - 20 = 80 liters
Remaining soda = 50 - 10 = 40 liters.

Step 5: Calculate the final quantities after adding pure juice.
Now, 10.02 liters (which is approximately 10 liters) of pure juice is added to the mixture.
New quantity of juice = 80 + 10 = 90 liters
New quantity of soda = 40 liters.

Step 6: Determine the final ratio of juice to soda.
The ratio of juice to soda in the resultant mixture is:
Juice : Soda = 90 : 40
Juice : Soda = 9 : 4.