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?
Let x litres of water be added.
Amount of acid in the solution = 45% of 1125 = 45 × 1125/100 = 506.25 litres.
Total volume after adding water = (1125 + x) litres.
Percentage of acid in the new mixture = 506.25/1125 + x × 100.
Given: 25 < 506.25 × 100/1125 + x < 30
⇒ 25(1125 + x) < 50625 < 30(1125 + x)
⇒ 28125 + 25x < 50625 < 33750 + 30x
From the left inequality: 25x < 22500 ⇒ x < 900
From the right inequality: 50625 < 33750 + 30x ⇒ 30x > 16875 ⇒ x > 562.5
∴ 562.5 < x < 900
Hence, the amount of water to be added is between 562.5 litres and 900 litres.