Question

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content? 

Answer 1

Let x litres of water be added to the 1125 litres of 45% solution of the acid.
Total quantity of mixture is (1125+x) litres.
Total acid content in 1125 litres of mixture = 45% of 1125 

\[\text{ It is given that the acid content in the resulting mixture must be more than 25 % and less than } 30 % . \]

\[ \therefore 25 % of\left( 1125 + x \right) < 45 % \times 1125 < 30 % of (1125 + x)\]

\[ \Rightarrow \frac{25}{100} \times \left( 1125 + x \right) < \frac{45}{100} \times 1125 < \frac{30}{100} \times \left( 1125 + x \right)\]

\[\text{ Multiplying throughout by }100: \]

\[28125 + 25x < 50625 < 33750 + 30x\]

\[ \Rightarrow x < \frac{50625 - 28125}{25} \text{ and } x > \frac{50625 - 33750}{30}\]

\[ \Rightarrow x < 900 \text{ and } x > 562 . 5\]

\[\text{ Thus, the water to be added should be more than 562 . 5 litres but less than 900 litres } . \]