If we mix the alcohol solution we have with pure water at the ratio 3:2, we will obtain a solution of 18% alcohol. If we instead mix them at a ratio of 4:1, what will be the alcohol percentage of the solution?

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rani01654 rani01654 · Answer 1 · 2019-12-02T07:42:51+01:00

Answer:

9%

Step-by-step explanation:

Let us assume that the original alcohol solution is x%.

So, when water and x% alcohol solution are mixed in the ratio 3 : 2, we will obtain a solution of 18% alcohol.

If water and x% alcohol solution are mixed in amount 3a and 2a amount, then we can write the equation as

[tex]\frac{2a\times \frac{x}{100} }{3a + 2a} = \frac{18}{100}[/tex]

⇒ [tex]\frac{2x}{5 \times 100} = \frac{18}{100}[/tex]

⇒ x = 45%

Now, water and 45% solution of alcohol are mixed in the ratio of 4 : 1, then the % of resulting alcohol solution will be

[tex]\frac{1 \times \frac{45}{100} }{4 + 1}\times 100 = 9%[/tex] (Answer)