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 there are $640$ litres of the $8\%$ solution, how many litres of $2\%$ solution will have to be added?

Answer 1

Let, the required quantity of 2% of boric acid= $x$ litres

So, quantity of mixtures= $(640+x)$ litres

The resulting mixture is to be more than 4% and less than 6% boric acid.

So, by the given condition,

8% of $640$ + 2% of $x$> 4% of $(640+x)$

$\Rightarrow \left(\frac{8}{100}\right)640+\left(\frac{2}{100}\right)x>\left(\frac{4}{100}\right)(640+x)$

$\Rightarrow 5120+2x>2560+4x$

$\Rightarrow 2560>2x$

$\Rightarrow x<1280......\left(1\right)$

and,

8% of 640 + 2% of $x$<6% of $(640+x)$

$\Rightarrow \left(\frac{8}{100}\right)640+\left(\frac{2}{100}\right)x<\left(\frac{6}{100}\right)(640+x)$

$\Rightarrow 5120+2x<3840+4x$

$\Rightarrow 1280<2x$

$\Rightarrow x>640......\left(2\right)$

From equations $\left(1\right)$ and $\left(2\right)$,

$640<x<1280$

Hence, the quantity of 2% boric acid lies between $640$ litres and $1280$ litres.