# 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 is required to be added.

Then, total mixture = (x + 1125) litres

It is evident that the amount of acid contained in the resulting mixture is 45% of 1125 litres.

This resulting mixture will contain more than 25% but less than 30% acid content.

$\therefore 30 \%$ of $(1125+x)>45 \%$ of 1125

And, $25 \%$ of $(1125+x)<45 \%$ of 1125

$30 \%$ of $(1125+x)>45 \%$ of 1125

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

$\Rightarrow 30(1125+x)>45 \times 1125$

$\Rightarrow 30 \times 1125+30 x>45 \times 1125$

$\Rightarrow 30 x>45 \times 1125-30 \times 1125$

$\Rightarrow 30 x>(45-30) \times 1125$

$\Rightarrow x>\frac{15 \times 1125}{30}=562.5$

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

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

$\Rightarrow 25(1125+x)<45 \times 1125$

$\Rightarrow 25 \times 1125+25 x<45 \times 1125$

$\Rightarrow 25 x<45 \times 1125-25 \times 1125$

$\Rightarrow 25 x<22500$

$\Rightarrow x<900$

\$\therefore 562.5

Thus, the required number of litres of water that is to be added will have to be more than 562.5 but less than 900.