1. Determine the required quantity of the total solution, which is given as 100 liters.
\text{Total Mixture} = 100\, \text{liters}
2. Find the proportion of lauryl in the total mixture.
\text{Percentage of lauryl} = 10\% = 0.10
3. Calculate the amount of lauryl sulfate needed.
\text{Amount of lauryl} = 0.10 \times 100\, \text{liters}
= 10\, \text{liters}
4. Therefore, the quantity of lauryl required for the best formula is 10 liters.
\text{Answer: 10 liters}