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Question:

A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1 : 3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S is

Explanation:

A 20% solution is mixed with x% solution in the ratio 1 : 3

Let 10 liters of 20% solution is mixed with 30 liters of x% solution.

Now, the total volume of the mixture = 40 liters.

This solution is mixed with 20% solution having equal volume.

∴ A total of 50 liters of 20% solutio is mixed with 30 liters of x% solution.

⇒ Final concentration = 31.25% = $\frac{20\%\times 50+x\times 30}{80}$

⇒ 2500 = 1000 + 30x
⇒ x = 50%

Hence, option (b).