Question

A 50ml after shave lotion at 30% alcohol is mixed with 30ml of pure water. What is the percentage of alcohol in the new solution?
(a) 18.75%
(b) 28.75%
(c) 38.75%
(d) 48.75%

Answer 1

Hint:
 First of all find the volume of alcohol in 30% alcohol after – shave lotion by considering the total volume of solution as 100ml. Now, use the unitary method to find the volume of alcohol in 50ml after shave lotion. In the next step find the total volume of a solution formed after the addition of 30ml pure water. Finally, apply the formula: - Percentage of alcohol in the new solution = (Volume of alcohol in the new solution / Volume of new solution) \[\times \] 100%.

Complete step by step answer:
Here, we have been provided with a 50ml after–shave lotion which contains 30% alcohol. We have to find the percentage of alcohol in the new solution which is formed by mixing 30ml of pure water in the lotion.
Now, we know that the percentage of any material in a given mixture is the parts of that material present in 100 parts of the mixture. So, let us apply this definition for the volume of alcohol in the mixture or lotion. So, we have 30% alcohol in the lotion.
\[\Rightarrow \] Volume of alcohol in 100ml lotion = 30ml
So, applying the unitary method we have,
\[\Rightarrow \] Volume of alcohol in 1ml lotion = \[\dfrac{30}{100}\]ml
\[\Rightarrow \] Volume of alcohol in 50ml lotion = \[\dfrac{30}{100}\times 50\]ml
\[\Rightarrow \] Volume of alcohol in 50ml lotion = 15ml
So, in the given 50ml after – shave lotion the volume of alcohol is 15ml. Now, when 30ml pure water is added in the lotion, we get,
\[\Rightarrow \] Total volume of new solution = 50ml + 30ml = 80ml.
Since, we have added only pure water therefore the volume of alcohol in the new solution will not change and only the total volume will be changed.
\[\Rightarrow \] Volume of alcohol in the new solution = Initial volume of alcohol
\[\Rightarrow \] Volume of alcohol in the new solution = 15ml
So, for the new solution we have,
\[\Rightarrow \] Total volume of lotion = 80ml
\[\Rightarrow \] Total volume of alcohol = 15ml
Applying the formula for percentage of alcohol in the new solution, we get,
\[\Rightarrow \] Required percentage = (Volume of alcohol / Volume of new solution) \[\times \] 100%.
\[\Rightarrow \] Required percentage = \[\dfrac{15}{80}\times 100%\]
\[\Rightarrow \] Required percentage = 18.75%
Hence, option (a) is the correct answer.

Note:
 One may note that we have not been provided with any information regarding the components of the lotion other than alcohol and water, so we have considered alcohol as the solute and water as the solvent. Always remember that the total volume of solution is the sum of the volume of solute and volume of solvent. So, in the percentage formula do not just consider the volume of solvent, i.e. water, in the denominator otherwise you will get the wrong answer.