How many litres of water will have to be added to 600 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.


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


>


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



460 > x


Now when,


45% of 600 < 30% of (x+600)


Multiplying both the sides by 100 in the above equation


<


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



300 < x


Thus, the amount of water required to be added ranges from 300 litres to 460 litres.


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