A manufacturer has 640 litres of a 8% solution of boric acid. How many litres of a 2% boric add solution be added to it so that the boric acid content in the resulting mixture will be more than 4% but less than 6%?

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Solution

Let x litres of 2% of boric acid be added to 640 litres of 8% solution of boric acid. Them total mixture = (640+x)litres

Boric acid content in this mixture $= (\frac{640 \times 8}{100} + \frac{x \times 2}{100})$ litres.

$∴ \frac{4}{100} \times (640 + x) < {\frac{640 \times 8}{100} + \frac{x \times 2}{100}} < \frac{6}{100} \times (640 + x)$

$\Rightarrow 2560 + 4 x < 5120 + 2 x < 3840 + 6 x$

$\Rightarrow 2 x < 2560 a n d 4 x > 1280 \Rightarrow 320 < x < 1280$ .

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