Impurity - glycerine

A sample of 50 L of glycerine is found to be adulterated to the extent of 20%. Find how much pure glycerine should be added to reduce impurity percentagerity to 5%.

Correct answer:

V₂ =  150 l

Step-by-step explanation:

$$\begin{gathered} V_1=50\text{l} \\ {r}_1=20\%=\frac{20}{100}=\frac{1}{5}=0.2 \\ {r}_2=5\%=\frac{5}{100}=\frac{1}{20}=0.05 \\ i=r_1\cdot V_1=0.2\cdot 50=10\text{l} \\ {r}_2=\frac{i}{V_1+V_2} \\ {r}_2\cdot (V_1+V_2)=i \\ {V}_2=\frac{i-r_2\cdot V_1}{r_2}=\frac{10-0.05\cdot 50}{0.05}=150\text{l} \end{gathered}$$

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