The amount of distilled water should the pharmacist add to make a 20 percent solution is 140 g.
Given-
Total weight of the solution is 56 grams.
The percentage of antiseptic in the given solution is 70 percent.
The percentage of the water in the given solution is total solution minus the percentage of antiseptic solution. As we know that the total solution is represent as 100 percent. Thus the percentage of the water in the given solution,
[tex]=100-70=30[/tex]
Therefore the percentage of the water in the given solution.
In the new solution the percentage of antiseptic is 20 percent. For this solution The percentage of the water,
[tex]=100-20=80[/tex]
Now the sum of the distilled water and the given solution (30 percent water solution) is equal to the sum of the distilled water and the 20 percent solution (80 percent water solution).Let [tex]x[/tex] be the quantity of the distilled water, we get,
[tex]x+\dfrac{30}{100} \times 56=\dfrac{80}{100} (56+x)[/tex]
[tex]x+0.3 \times 56=0.8(56+x)[/tex]
[tex]x+16.8=44.8+0.8x[/tex]
[tex]x-0.8x=44.8-16.8[/tex]
[tex]0.2x=28[/tex]
[tex]x=\dfrac{28}{0.2}[/tex]
[tex]x=140[/tex]
Hence, the amount of distilled water should the pharmaceutics add to make a 20 percent solution is 140 g.
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