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?

Solution:

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.

Therefore,

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)

⇒ 2/100 x + 8/100 (640) > 4/100 (x + 640)

⇒ 2x + 5120 > 4x + 2560

⇒ 5120 - 2560 > 4x - 2x

⇒ 2560 > 2x

⇒ x < 1280 ....(1)

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

⇒ 2/100 x + 8/100 (640) < 6/100 (x + 640)

⇒ 2x + 5120 < 6x + 2560

⇒ 5120 - 2560 < 6x - 2x

⇒ 2560 < 3x

⇒ x > 320 ....(2)

From (1) and (2), we get, 320 < x < 1280

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 litres

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NCERT Solutions Class 11 Maths Chapter 6 Exercise ME Question 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?

Summary:

Linear inequations situation is given. We have found that 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 litres