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?
Given, the volume of existing solution is 1125 liters.
The amount of acid contained in the solution is,
45 % o f 1125 = 45 100 × 1125 = 0.45 × 1125 = 506.25
Now, let the amount of water added in the solution be x liters.
Volume of new solution = 1125 + x
As it is given that the resulting solution contains minimum of 25 % acid.
25 % of ( 1125 + x ) < 45 % of 1125 25 100 × ( 1125 + x ) < 506.25 ( 1125 + x ) 4 < 506.25 1125 + x < 506.25 × 4
Solve further,
1125 + x < 2025 x < 2025 − 1125 x < 900
As it is given that the resulting solution contains maximum of 30 % acid content.
30 % of ( 1125 + x ) > 45 % of 1125 30 100 × ( 1125 + x ) > 506.25 3 10 × ( 1125 + x ) > 506.25 3 ( 1125 + x ) > 506.25 × 10
Solve further,
1125 + x > 5065 3 x > 1687.5 − 1125 x > 562.5
The value of x lies between 562.5 < x < 900 .
Therefore, the amount of water added must be to the solution is more than 562.5 liters but less than 900 litres.
Given, the volume of existing solution is
The amount of acid contained in the solution is,
Now, let the amount of water added in the solution be x liters.
Volume of new solution
As it is given that the resulting solution contains minimum of
Solve further,
As it is given that the resulting solution contains maximum of
Solve further,
The value of x lies between
Therefore, the amount of water added must be to the solution is more than 562.5 liters but less than 900 litres.
