Q. 124.0( 71 Votes )

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?

Answer :

8% of solution of boric acid = 640 litres


Let x litres of 2% boric acid solution is added


Total mixture = x + 640 litres


The resulting mixture has to be more than 4% but less than 6% boric acid.


2% of x + 8% of 640 > 4% of (x + 640) and


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


2% of x + 8% of 640 > 4% of (x + 640)



2x + 5120 > 4x + 2560


5120 – 2560 > 4x – 2x


2560 > 2x


x < 1280 ….(I)


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



2x + 5120 < 6x + 3840


6x – 2x > 5120 – 3840


4x > 1280


x > 320 ……….(II)


From (I) and (II)


320 < x < 1280


the number of litres of 2% of boric acid solution that has to be added will be more than 320 litres but less than 1280 litres.


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