This problem involves calculating the final concentration (percentage) of spirit in a mixture after adding water.
Calculating Spirit Percentage in Mixture
We need to find the new percentage of spirit after adding water to the initial mixture. The amount of spirit remains constant, but the total volume increases.
Step 1: Calculate the Initial Volume of Spirit
The initial mixture has a volume of 50 L and contains 20% spirit. The volume of spirit is:
Initial Spirit Volume = Total Volume $\times$ Percentage of Spirit
Initial Spirit Volume = $50 \, \text{L} \times \frac{20}{100}$
Initial Spirit Volume = $50 \, \text{L} \times 0.20 = 10 \, \text{L}$
Step 2: Calculate the Total Volume of the Resulting Mixture
10 L of water is added to the initial 50 L mixture.
Resulting Mixture Volume = Initial Volume + Added Water
Resulting Mixture Volume = $50 \, \text{L} + 10 \, \text{L}$
Resulting Mixture Volume = $60 \, \text{L}$
Step 3: Calculate the Final Percentage of Spirit
The volume of spirit (10 L) remains the same, but the total volume is now 60 L. The new percentage is:
Final Spirit Percentage = $\left( \frac{\text{Volume of Spirit}}{\text{Resulting Mixture Volume}} \right) \times 100$
Final Spirit Percentage = $\left( \frac{10 \, \text{L}}{60 \, \text{L}} \right) \times 100$
Final Spirit Percentage = $\frac{1}{6} \times 100$
Final Spirit Percentage = $\frac{100}{6} \% = \frac{50}{3} \% = 16\frac{2}{3}\%$
Therefore, the percentage of spirit in the resulting mixture is $16\frac{2}{3}\%$.
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