In a chemistry lab, there is some quantity of $\displaystyle 50$% acid solution and some quantity of $\displaystyle 25$% acid solution. How much of each should be mixed to make $\displaystyle 10$ litres of $\displaystyle 40 \%$ acid solution ?

Let quantity of $\displaystyle 50$% and of $\displaystyle 25$% acid solution be ' \(\displaystyle x\) ' \(\displaystyle l\) and ' \(\displaystyle y\) ' \(\displaystyle l\) respectively. \[\text { Therefore, } x+y=10 \] and \(\displaystyle \frac{50}{100} \times x+\frac{25}{100} \times y=\frac{40}{100} \times 10\) or \(\displaystyle 2 x+y=16\)---- (ii) Solving (i) and (ii) to get \(\displaystyle x=6, y=4\) Hence, \(\displaystyle 6 l\) of $\displaystyle 50$% and \(\displaystyle 4 l\) of $\displaystyle 25$% acid solution are mixed.