Question:
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?
Answer:
Given mixture = 640 litres
Let 2% boric acid solution is x litre.
So total amount of mixture = 640 + x.
Now given in the question
2% of x + 8% of 640 > 4% of (640 + x)
=> 2x/100 + (8*640)/100 > {4*(640 + x)}/100
=> 2x + 5120 > 2560 + 4x
=> 2x - 4x > 2560 - 5120
=> -2x > -2560
=> 2x < 2560
=> x < 2560/2
=> x < 1280
Again from the question
2% of x + 8% of 640 < 6% of (640 + x)
=> 2x/100 + (8*640)/100 < {6*(640 + x)}/100
=> 2x + 5120 < 3840 + 6x
=> 2x - 6x < 3840 - 5120
=> -4x < -1280
=> 4x > 1280
=> x > 1280/4
=> x > 320
Hense number of litres of the 2% solution added is between 320 litres and 1289 litres.
Not what you are looking for? Go ahead and submit the question, we will get back to you.
