Question

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution in it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 liters of the 8% solution. How many liters of the 2% solution will have to be added.

Answer 1

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 + xtotal 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 mixture4/100(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 + 6x4*640+4x <640*8 + 2x 640*8 +2x <6*640 +6x4*640 +4x -2x <640*8 640*8 +2x -6x < 6*6402x< 640*8 -640*4 -4x < 640*6 -640*8x< 640(8-4)/2 -x< 640(6-8) /4x<640*4 /2 -x< 640*-2/4x < 640*2 = 1280 x> 320so, x lies between 320l to 1280l.

Answer 2

Answer:Let x litres of 2% boric acid solution is required to be added. Then, total mixture = (x + 640) litres This resulting mixture is to be more than 4% but less than 6% boric acid. 2%x + 8% of 640 > 4% of (x + 640) and 2% x + 8% of 640 < 6% of (x + 640) 2%x + 8% of 640 > 4% of (x + 640) Thus, the number of litres of 2% of boric acid solution that is to be added will have to be more than 320 litres but less than 1280

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Explanation: