Question

From 5 liters of 20% solution of alcohol in water 2 liters of the solution is taken out and 2 liters of water is added to it. So, find the strength of alcohol in the new solution.
A. 12%
B. 15%
C. 16%
D. 18%

Answer 1

Hint: First we will analyze the question and apply the given conditions in the question one by one. We will first remove 2 liters from the total amount and then find out the amount of alcohol already present by finding 20% of the remaining solution. After adding 2 liters of water, again we will find the amount of alcohol in the final solution.

Complete step-by-step solution:
It is given that there is a total of 5 liters of solution and we are given that 2 liters of the solution are taken out. Therefore, the remaining solution is
$ \Rightarrow 5 - 2 = 3$ liters
Now, it is given that there is 20% alcohol in the solution since there are 3 liters of solution. Therefore, the amount of alcohol in 3 liters solution,
$ \Rightarrow \dfrac{{20}}{{100}} \times 3 = \dfrac{{60}}{{100}}$
On simplifying the terms, we get
$ \Rightarrow \dfrac{{20}}{{100}} \times 3 = \dfrac{3}{5}$ liters
Now, after adding 2 liters of water again, the amount of solution becomes 5 liters again but with different strengths. Now, we have 5 liters of the solution in which $\dfrac{3}{5}$ liters is alcohol.
So, now the percentage of alcohol in 5 liters solution is as follows:
$ \Rightarrow \dfrac{{\dfrac{3}{5}}}{5} \times 100 = \dfrac{3}{{5 \times 5}} \times 100$
On simplifying the terms, we get
$ \Rightarrow \dfrac{{\dfrac{3}{5}}}{5} \times 100 = 12$
Therefore, the strength of alcohol in the new solution is 12%.

Hence, option (A) is the correct answer.

Note: Remember that while finding the percentage we use the formula:
$\dfrac{{{\text{Amount of alcohol}}}}{{{\text{Total amount of solution}}}} \times 100$
Always, put a percentage sign at the end every time you use it to show it. A common mistake made is we sometimes forget to mention the unit so always do mention it.