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.