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 1

Let x litres of 2% boric acid solution is required to be added.
Then, total mixture = (x + 640) litres 
This resulting mixture is to be more than 4% but less than 6% boric acid.
∴ 2%x + 8% of 640 > 4% of (x + 640) and 2% x + 8% of 640 < 6% of (x + 640) 
2%x + 8% of 640 > 4% of (x + 640)
\(⇒ \frac{2}{100}x + \frac{8}{100}(640) > \frac{4}{100}(x+640)\)
⇒ 2x + 5120 > 4x + 2560 
⇒ 5120 – 2560 > 4x – 2x 
⇒ 5120 – 2560 > 2x 
⇒ 2560 > 2x 
⇒ 1280 > x 
2% x + 8% of 640 < 6% of (x + 640)
\(⇒\frac{ 2}{100}x +\frac{ 8}{100}(640) < \frac{6}{100}(x+640)\)
⇒ 2x + 5120 < 6x + 3840 
⇒ 5120 – 3840 < 6x – 2x 
⇒ 1280 < 4x 
⇒ 320 < x 
∴ 320 < x < 1280 
Thus, the number of litres of 2% of boric acid solution that is to be added will have to be more than 320 litres but less than 1280 litres.