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 addedd

As we require a solution less than 6% and 4% so for convenience we take the final solution as 5%.
As 640 litre of 8% solution is there , let the second solution of x litres be 2 %
Hence doing boric acid balance, we have
$\frac{{\displaystyle \frac{8}{100}}\times 640 +x\times {\displaystyle \frac{2}{100}}}{640+x}=5\%$
(8 ⨯640 + 2x)/(640 + x ) = 5
So 5 ⨯640 + 5x = 8 ⨯640 + 2x
Or 3x = 3⨯ 640
Or x = 640 litres.

So we have to add 640 litres of 2% solution.