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 there are 640litres of the 8% solution, how many litres of 2% solution will have to be added?

Explanation

vol of `8% BA= 640 L`

vol of `2% BA= xl`

`n_1v_1 + n_2v_2= n_3v_3`

`1/(v_1+v_2) (n_1v_1 + n_2v_2) = n_3`

`1/(600+x) [ 8% xx 600 + 2% xx x] = n_3`

`4% < 1/(600+x) [ 8% xx 640 + 2% x] < 6%`

`4/100 xx(640 +x) < 8/100 xx 640 + 2x/100 < 6/100(640 + x)`

`(2560 + 4x)/100 < (5120 + 2x)/100< (3840 + x)/100`

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