Question

A certain volume of a solution 90% pure acid and 10% water is mixed with another solution containing 97% acid and 3% water If the mixture obtained is 21 litres of 95% acid solution, what is the difference between the volumes of the two solutions mixed?

Answer 1

Two different mixtures were mixed.  The resulting solution contains 95% acid solution.

i.e. 95% of 21 litres = 19.95 litres.

Let I solution be of volume x and ii of volume y.

The two are mixed.

Acid content in the first would be = 0.9x and second = 0.97y

We have 0.9x +0.97 y = 19.95  ... (i)

And x+y = 21 ...(ii)

Solve (i) and (ii)

Multiply (ii) by 0.9 to have 0.9x+0.9y = 18.9  ...(iii)

(i)-(iii) gives   0.07y = 1.05

y = 15 litres and x = 6 litres.

6 litres of I mix and 15 litres of II mix should be mixed.