Question

A quantity of 30 ml of 20% alcohol is mixed with 20 ml of 25% alcohol What is the strength of alcohol in the mixture?
(A) 20%
(B) 27%
(C) 30%
(D) 22%

Answer 1

Hint: We solve this question by first considering the first quantity. Then we find the volume of alcohol in the first quantity by multiplying the given volume with the given percentage. Then we consider the second quantity and find the volume of alcohol in it in the same procedure as above. Then as they are mixed, we add the volumes of quantities and find the total volume of mixture. Then we add the volume of alcohols we have obtained to find the volume of alcohol in the mixture. Then from the obtained values we find the percentage of alcohol in the mixture, that is strength of alcohol in the mixture.

Complete step-by-step answer:
We are given that there are two different quantities and they are mixed together.
First quantity is 30 ml with 20% alcohol and the second quantity is 20ml with 25% alcohol.
So, first let us consider the first quantity.
Volume of the first quantity is 30 ml.
Let us find the volume of the alcohol.
As it is given that it has 20% alcohol, volume of alcohol is equal to 20% of 30ml.
So, we get the volume of alcohol as,
$\begin{align}
  & \Rightarrow \dfrac{20}{100}\times 30 \\
 & \Rightarrow \dfrac{600}{100} \\
 & \Rightarrow 6 \\
\end{align}$
So, we get the volume of alcohol in the first quantity as 6 ml.
Now let us consider the second quantity.
Volume of the second quantity is 20 ml.
Let us find the volume of the alcohol.
As it is given that it has 25% alcohol, volume of alcohol is equal to 25% of 20ml.
So, we get the volume of alcohol as,
$\begin{align}
  & \Rightarrow \dfrac{25}{100}\times 20 \\
 & \Rightarrow \dfrac{500}{100} \\
 & \Rightarrow 5 \\
\end{align}$
So, we get the volume of alcohol in the first quantity as 5 ml.
We are given that these two quantities are mixed. Then we get,
Total Volume = Volume of first quantity + Volume of second quantity
$\begin{align}
  & \Rightarrow 30+20 \\
 & \Rightarrow 50 \\
\end{align}$
So, we get that the total volume is 50ml.
Now let us find the total volume of alcohol.
Total Volume of alcohol = Volume of alcohol in first quantity + Volume of alcohol in second quantity
So, we get,
$\begin{align}
  & \Rightarrow 6+5 \\
 & \Rightarrow 11 \\
\end{align}$
So, the volume of alcohol is 11 ml.
So, after mixing there is 11 ml of alcohol in 50ml.
Then the percentage of alcohol is,
$\begin{align}
  & \Rightarrow \dfrac{11}{50}\times 100 \\
 & \Rightarrow 11\times 2 \\
 & \Rightarrow 22\% \\
\end{align}$
So, the strength of alcohol in the mixture is 22%.
Hence the answer is Option D.

So, the correct answer is “Option D”.

Note: There is a possibility of one making a mistake while solving this question by adding the percentages of alcohol directly without converting them into volume. But it is wrong. As they are different quantities, we need to convert them into volume and then add them to find the total volume of alcohol in the mixture.