Given:
Volume of acid solution = 1125 litres
Percentage of acid = 45%
Amount of acid present
= 45% of 1125
= 506.25 litres
Let:
x litres of water be added.
Total volume of new solution = (1125 + x) litres
Condition 1: Acid content more than 25%
Acid percentage > 25%
\(\frac{506.25}{1125 + x} > \frac{25}{100}\)
506.25 > 0.25(1125 + x)
506.25 > 281.25 + 0.25x
225 > 0.25x
x < 900
Condition 2: Acid content less than 30%
Acid percentage < 30%
\(\frac{506.25}{1125 + x} < \frac{30}{100}\)
506.25 < 0.30(1125 + x)
506.25 < 337.5 + 0.30x
168.75 < 0.30x
x > 562.5
Final Answer:
To satisfy both conditions,
562.5 litres < x < 900 litres
Hence, the quantity of water to be added must be
more than 562.5 litres but less than 900 litres.