A solution of 8 % boric acid is to be diluted | vedclass

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(A) Let $x$ litres of $2 \%$ boric acid solution be added.Total volume of the mixture $= (x + 640)$ litres.Amount of boric acid in the mixture $= (0.0

Vedclass · Accepted Answer

$320 < x < 1280$

Vedclass · Answer

(A) Let $x$ litres of $2 \%$ boric acid solution be added.Total volume of the mixture $= (x + 640)$ litres.Amount of boric acid in the mixture $= (0.02x + 0.08 	imes 640) = (0.02x + 51.2)$ litres.The concentration of the resulting mixture must be between $4 \%$ and $6 \%$.Condition $1$: $\frac{0.02x + 51.2}{x + 640} > 0.04$$0.02x + 51.2 > 0.04x + 25.6$$51.2 - 25.6 > 0.04x - 0.02x$$25.6 > 0.02x \Rightarrow x Condition $2$: $\frac{0.02x + 51.2}{x + 640} $0.02x + 51.2 $51.2 - 38.4 $12.8  320$.Thus,the amount of $2 \%$ solution to be added is between $320$ litres and $1280$ litres.

$A$ 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,how many litres of the $2 \%$ solution will have to be added?

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