#### 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?

#### Solution

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)

⇒ 2*x* + 5120 > 4*x* + 2560

⇒ 5120 – 2560 > 4*x* – 2*x*

⇒ 5120 – 2560 > 2*x*

⇒ 2560 > 2*x*

⇒ 1280 > *x*

*2% x + 8% of 640 < 6% of (x + 640)*

⇒ 2*x* + 5120 < 6*x* + 3840

⇒ 5120 – 3840 < 6*x* – 2*x*

⇒ 1280 < 4*x*

⇒ 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.