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 contact ?

Answer 1

Let the quantity of water to be added to solution =x liters

$\therefore 25\%(1125+x)<45\%of1125\Rightarrow \frac{25}{100}(1125+x)<\frac{45}{100}\times 1125\Rightarrow 1125+x<\frac{45}{100}\times 1125\Rightarrow 1125+x<45\times 45\Rightarrow 1125+x<2025\Rightarrow x<2025-1125\Rightarrow x<900and45\%of1125<30\%(1125+x)\Rightarrow \frac{45}{100}\times 1125<\frac{30}{100}(1125+x)\Rightarrow \frac{45}{30}\times 1125<1125+x\Rightarrow \frac{3}{2}\times 1125<1125+x\Rightarrow 1.5\times 1125<1125+x\Rightarrow 1687.5<1125+x\Rightarrow 168.75-1125<x\Rightarrow 562.5<x...\left(ii\right)$

Using (i) and (ii), we get 562.5<x<900

Hence,quantity of water lies between 562.5 litres and 900 litres.