How many litres of water will have to be added to 600 litres of the 45% solution of acid so that the resulting mixture will contain more than 25%, but less than 30% acid content?

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Solution

Let x litres of water may be added. Then,

$25 % o f (600 + x) < \frac{600 \times 45}{100} < 30 % o f (600 + x)$

$\Rightarrow \frac{600 + x}{4} < 270 < \frac{1800 + 3 x}{10}$

$\Rightarrow \frac{600 + x}{4} < 270 < \frac{1800 + 3 x}{10} > 270$

$\Rightarrow 600 + x < 1080 a n d 1800 + 3 x > 2700 \Rightarrow 300 < x < 480$

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How many litres of water will have to be added to 600 litres of the 45% solution of acid so that the resulting mixture will contain more than 25%, but less than 30% acid content?

Let x litres of water may be added. Then, 25% of (600+x)<600×45100<30% of (600+x) ⇒600+x4<270<1800+3x10 ⇒600+x4<270<1800+3x10>270 ⇒600+x<1080 and 1800+3x>2700⇒300<x<480