How many litres of water will have to be added to 1125 litres of the 45%

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?

Solution:

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

It is given that the acid content in the resulting mixture must be more than $25 \%$ and less than $30 \%$.

$\therefore 25 \%$ of $(1125+x)<45 \% \times 1125<30 \%$ of $(1125+x)$

$\Rightarrow \frac{25}{100} \times(1125+x)<\frac{45}{100} \times 1125<\frac{30}{100} \times(1125+x)$

Multiplying throughout by 100 :

$28125+25 x<50625<33750+30 x$

$\Rightarrow x<\frac{50625-28125}{25}$ and $x>\frac{50625-33750}{30}$

$\Rightarrow x<900$ and $x>562.5$

Thus, the water to be added should be more than $562.5$ litres but less than 900 litres.