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 2% solution will have to be added?

let the 2% soution added is xlt.

after adding 2% of bric accid in the solution to the mixturetotal amount of solution left is = 640 + x

total amount of acid in the soution is = 640*8% + x*2%

acc. to ques. total amount of mixture is to be within 4% to 6%

equ. becomes 4% of mixture < amount of acid in the mixture < 6% of mixture

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

100 cancel out in all.

4*640 +4x < 640*8 + 2x < 6*640 + 6x

4*640+4x <640*8 + 2x 640*8 +2x <6*640 +6x

4*640 +4x -2x <640*8 640*8 +2x -6x < 6*640

2x< 640*8 -640*4 -4x < 640*6 -640*8

x< 640(8-4)/2 -x< 640(6-8) /4

x<640*4 /2 -x< 640*-2/4

x < 640*2 = 1280 x> 320

so, x lies between 320l to 1280l.