Question

A chemist has one solution which is 50% acid and second which is 25% acid. How much of each should be mixed to form 10 litres of 40% acid solutions

Answer 1

Hint: We can obtain linear equations according (by assigning variables to the required values of respective liquids) to the question and calculate the assumed values of the respective solutions by calculating these.
Percentage to fraction:
A % = $\dfrac{A}{{100}}$

Complete step-by-step answer:
Let the amount of the two solutions to be mixed be x litres and y litres respectively.
The amount (in litres) of acid solution to be prepared is 10 litres, so:
x + y = 10 _________ (1)
Since both the solutions together will make 10l of acid solution
Now, according to the question:
50 % of the first solution is acidic, 25 % of the second solution is acidic, and these are mixed to form a 40% acidic solution of 10 litres.
50 % of x + 25 % of y = 40 % of 10
In terms of fraction this can be written as:
\[\Rightarrow \dfrac{{50}}{{100}} \times x + \dfrac{{25}}{{100}} \times y = \dfrac{{40}}{{100}} \times 10\]
50x + 25y = 400 (100s in denominator gets cancelled)
Dividing both sides with 5 for simplification:
10x + 5y = 80 ________ (2)
Calculating the value of x and y using (1) and (2):
$\Rightarrow$ x + y = 10
$\Rightarrow$ 10x + 5y = 80
Multiplying (1) with 5, then:
$\Rightarrow$ 10x + 5y = 80
$\Rightarrow$ 5x + 5y = 50
Subtracting the two, we get:
$\Rightarrow$ 5x = 30
$\Rightarrow x = \dfrac{{30}}{5}$
$\Rightarrow$ x = 6
Substituting this value of x in (1):
$\Rightarrow$ 6 + y = 10
$\Rightarrow$ y = 10 – 6
$\Rightarrow$ y = 4
The amount of respective solutions were x and y litres.
Therefore, 6 litres of the first solution and 4 litres of the second solution should be mixed for the preparation of required acid solution..

Note: The equations formed are called linear equations in two variables because there are 2 assumed variables and the highest power of these variables is 1.
Percentage refers to a part per 100 parts, so when the percentage gets converted to fraction, it is done with respect to 100. As percentages do not have any dimensions, they are called dimensionless.