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Misc 12 - A solution of 8% boric acid is to be diluted by adding

Misc 12 - Chapter 6 Class 11 Linear Inequalities - Part 2


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Misc 12 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? 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% 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) 2/100 x + 8/100 (640) > 4/100 (x + 640) 2x + 5120 > 4x + 2560 5120 – 2560 > 4x – 2x 2560 > 2x 1280 > x x < 1280 2% x + 8% of 640 < 6% of (x + 640) 2/100 x + 8/100 (640) > 6/100 (x + 640) 2x + 5120 < 6x + 3840 5120 – 3840 < 6x – 2x 1280 < 4x 320 < x x > 320 Thus, x < 1280 & x > 320 ∴ 320 < x < 1280 Thus, the number of litres of 2% of boric acid solution that is to be added wall have to be more than 320 litres but less than 1280 litres.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.