Question

90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution.
Find the quantity of each type of acids to be mixed to form the mixture.

Answer 1

Let x litres and y litres be respectively the amount of 90% and 97% pure acid solutions.
As per the given condition
$$\begin{gathered} 0.90x+0.97y=21\times 0.95 \\ \Rightarrow 0.90x+0.97y=21\times 0.95.....\left(i\right) \end{gathered}$$
And
$x+y=21.....\left(ii\right)$
From (ii), subtitute $y=21-x$ in (i) to get
$$\begin{gathered} 0.90x+0.97\left(21-x\right)=21\times 0.95 \\ \Rightarrow 0.90x+0.97\times 21-0.97x=21\times 0.95 \\ \Rightarrow 0.07x=0.97\times 21-21\times 0.95 \\ \Rightarrow x=\frac{21\times 0.02}{0.07}=6 \end{gathered}$$
Now, putting x = 6 in (ii), we have
$6+y=21\Rightarrow y=15$
Hence, the required quantities are 6 litres and 15 litres.