A manufacturer has 600 L of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that the acid content in the resulting mixture will be more than 15% but less than 18%?

Let x litres of 30% acid solution is required to be added. Then
Total mixture = (x + 600) litres
Therefore 
30% x + 12% of 600 > 15% of (x + 600)
and 30% x + 12% of 600 < 18% of (x + 600)
or 30x100+12100600>15100x+600and 30x100+12100600<18100x+600or 30x+7200>15x+9000and 30 x +7200<18x+10800or 15x>1800 and 12x<3600or x >120 and x<300So 120<x<300Thus , the number of liters of the 30% solution of acid will have to be morethan 120 liters but less than 300 litres.

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