I have tried this question by ratio method and I am getting my answer as 35.29% but they say this is wrong. Please help
A solution of hydrochloric acid and sulphuric acid has 40% of hydrochloric acid . A solution of hydrochloric acid and nitric acid has a composition ratio of 2:7. These two solutions are mixed in a way that the new solution formed has more sulphuric acid than nitric acid and hydrochloric acid constitutes x% of this solution. What can be the minimum value of x?
Thanks
Suppose we take a volume A of the first mixture, and a volume $B$ of the second mixture. Then in the final mixture there will be 3/5A of sulphuric acid, 7/9B of nitric acid and 2/5A+2/9B of hydrochloric acid. Hence, the final proportion of hydrochloric acid is (2/5A+2/9B)/(A+B). We also know that there can be no more nitric acid than sulphuric acid in the final mixture, thus 7/9B<3/5A .
You can now check that the minimum is obtained when the nitric acid is just less than the sulphuric acid, or when 7/9B=3/5A. Working the math out, you should get that the minimum proportion of hydrochloric acid is 20/62=0.3225806.