Question

A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each
should be used to make 10 litres of a 40% acid solution?

Answer 1

Let x litres and y litres be the amount of acids from 50% and 25% acid solutions respectively.
As per the question
$$\begin{gathered} 50\%\mathrm{of}x+25\%\mathrm{of}y=40\%\mathrm{of}10 \\ \Rightarrow 0.50x+0.25y=4 \\ \Rightarrow 2x+y=16.....\left(i\right) \end{gathered}$$
Since, the total volume is 10 litres, so
$x+y=10.....\left(ii\right)$
Subtracting (ii) from (i), we get
$x=6$
Now, putting x = 6 in (ii), we have
$6+y=10\Rightarrow y=4$
Hence, volume of 50% acid solution = 6 litres and volume of 25% acid solution = 4 litres.