Question

A 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution?

Answer 1

Hint: First, we will find the total amount of mixture by adding 50ml of after-shave lotion and 30ml of pure water. Then we will assume that there is ‘x’ amount of alcohol in the final solution. Then, we will equate 30% of alcohol in 50ml after-shave lotion to ‘x’ amount of alcohol in the final solution. Thus, on solving this we will get our answer of ‘x’. Then we will multiply it with 100 to get a percentage value.

Complete step by step answer:
Here, we are given 50 ml of after-shave lotion is mixed with 30 ml of pure water. So, we have total amount of mixture as
$50ml+30ml=80ml$
Now, we are given that there is 30% alcohol in 50ml after-shave lotion. We will assume that there is ‘x’ amount of alcohol in the final solution. So, we can write it the amount of alcohol in after-shave lotion is equal to the amount of alcohol in the final. So, in mathematical terms, we can write it as
$30\%of\left( 50 \right)=x\left( 80 \right)$
On solving, we get as
$\Rightarrow \dfrac{30}{100}\cdot 50=80x$
$\Rightarrow 15=80x$
On dividing both sides by 80, we will get as
$\Rightarrow \dfrac{15}{80}=x$
$\Rightarrow x=0.1875$
To convert this into percentage, we have to multiply it with 100. So, we will get
$\Rightarrow x=0.1875\times 100=18.75\%$
Thus, the percentage of alcohol in the new solution is 18.75%.

Note: Another method to solve this problem is first we find out 30% of 50ml which we will get as 15ml. Now, we know that the total solution we have is 80ml. So, the percentage of alcohol in the final solution is $\dfrac{15}{80}\times 100=18.75\%$ . Thus, we get the same answer.
Also, this is a little bit tricky to understand that the amount of alcohol present in solution will be equal to the final solution also. Otherwise mistakes happen when students consider that 30% is present before mixing them, the same 30% will be there after mixing the solution. So, the direct answer will be 30% which will be wrong. So, do not make this mistake. Understand the question first and then try to solve it.