Pharmacist

Pharmacist had a 12 l vessel herbal lotion, which contained 30% active ingredient. Her assistant poured 18 liters of herbal lotion containing 45% of the active ingredient into a container. What percentage of herbal lotion was produced?

Correct result:

p =  39 %

Solution:

$$\begin{gathered} V_1=12\text{ l } \\ {p}_1=30\mathrm{\%}={\displaystyle \frac{30}{100}}=0.3 \\ {V}_2=18\text{ l } \\ {p}_2=45\mathrm{\%}={\displaystyle \frac{45}{100}}=0.45 \\ p=100\cdot {\displaystyle \frac{p_1\cdot V_1+p_2\cdot V_2}{V_1+V_2}}=100\cdot {\displaystyle \frac{0.3\cdot 12+0.45\cdot 18}{12+18}}=39\mathrm{\%} \end{gathered}$$

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