Let x litres of water be added.
Then total mixture = x + 600
Amount of acid contained in the resulting mixture is 45% of 600 litres.
It is given that the resulting mixture contains more than 25% and less than 30% acid content.
Therefore,
45% of 600 > 25% of (x + 600)
And
30% of (x+600) > 45% of 600
When,
45% of 600 > 25% of (x+600)
Multiplying both the sides by 100 in above equation
\(\frac{45}{100} \times 600 \) > \(\frac{25}{100} \times\) (x + 600)
45 × 600 > 25(x + 600)
27000 > 25x + 15500
Subtracting 15500 from both the sides in above equation
27000 – 15500 > 25x + 15500 – 15500
11500 > 25x
Dividing both the sides by 25 in above equation
\(\frac{11500}{25} > \frac{25{\text{x}}}{25}\)
460 > x Now when,
45% of 600 < 30% of (x+600)
Multiplying both the sides by 100 in the above equation
\(\frac{45}{100} \times 600 < \frac{30}{100} \times ({\text{x}} + 600)\)
45 × 600 < 30(x + 600)
27000 < 30x + 18000
Subtracting 18000 from both the sides in above equation
27000 – 18000 < 30x + 18000 – 18000
9000 < 30x
Dividing both the sides by 30 in above equation
\(\frac{900}{30} > \frac{30{\text{x}}}{30}\)
Thus, the amount of water required to be added ranges from 300 litres to 460 litres.