Question

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, have many litres of the 2% solution will have to be added?

Answer 1

Let x litre of 2% boric acid solution be added to 640 litres of 8% boric acid solution. Then Total quanity of mixture =(640+x) litres Total boric acid in (640+x)litres of mixture

$=\frac{2x}{100}+\frac{8}{100}\times 640=\frac{x}{50}+\frac{256}{5}$

It is given that the resulting mixture must be more than 4% but less than 6% boric acid.

$\therefore \frac{4}{100}(640+x)<\frac{x}{50}+\frac{256}{5}<\frac{6}{100}(640+x)$

$\Rightarrow \frac{640+x}{25}<\frac{x+2560}{50}<\frac{1920+3x}{50}$

$\Rightarrow 1280+2x<x+2560<1920+3x$

$\Rightarrow 1280+2x<x+2560$

and x+2560 < 1920 +3x

$\Rightarrow x<1280$ and -2x < -640

$\Rightarrow x<1280$ and x > 320

$\Rightarrow 320<x<1280$

Thus 2% boric acid solution must be more than 320 litres but less than 1280 litres.