Question

A chemist needs to strengthen a 15% alcoholic solution to one of 32% alcoholic. How much pure alcohol should be added to 800ml of 15% solution?

Answer 1

Hint: We have to change the concentration of alcohol of 800ml solution by adding ‘x’ ml of pure alcohol. We will use percentages concept for calculations.

Complete step-by-step answer:
From the given information, we have 800ml of solution with 15% alcohol.
The alcohol in 800ml solution = $800 \times \dfrac{{15}}{{100}} = 120ml$
Now we need to add some pure alcohol to this 800ml to change the alcohol percentage to 32%.
Let ‘x’ ml of pure alcohol (100% alcohol) is added.
Then our resulting solution = (800 + x) ml
Amount of alcohol in the resulting solution = (120 + x) ml
We want the alcohol percentage as 32%.
$ \Rightarrow \dfrac{{Amount\;of\;alcohol}}{{Total\;amount\;of\;solution}} \times 100 = 32$
$ \Rightarrow \dfrac{{x + 120}}{{800 + x}} \times 100 = 32$
On simplification of the above equation,
$\eqalign{
  & \Rightarrow 100x + 12000 = 32x + 25600 \cr
  & \Rightarrow 100x - 32x = 25600 - 12000 \cr
  & \Rightarrow 68x = 13600 \cr} $
$ \Rightarrow x = \dfrac{{13600}}{{68}} = 200$
$\therefore $ The amount of pure alcohol to be added is 200ml.

Note: While solving these kinds of problems, we need to clearly understand the given information. We have to form algebraic equations for calculating the required values.