NCERT Class XI Mathematics - Linear Inequalities - Solutions
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Question : 63
Total: 65
A solution 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 8% solution, how many litres of the 2% solution will have to be added?
Solution:
Let the 2% boric acid solution be x litres.
∴ Mixture is (640 + x) litre.
(i) Now, 2% of x + 8% of 640 > 4% of (640 + x)
⇒
+
or 5120 – 2560 > 4x – 2x
or, 2x < 2560 or x < 1280 ... (1)
(ii) 2% of x + 8% of 640 < 6% of (640 + x)
or
+
⇒ 5120 – 3840 < 6x – 2x
⇒ 4x > 1280 or x > 320 ... (2)
From (1) and (2), we have 320 < x < 1280
Thus, the number of litres to be added, should be greater than 320 litres and less than 1280 litres.
∴ Mixture is (640 + x) litre.
(i) Now, 2% of x + 8% of 640 > 4% of (640 + x)
⇒
or 5120 – 2560 > 4x – 2x
or, 2x < 2560 or x < 1280 ... (1)
(ii) 2% of x + 8% of 640 < 6% of (640 + x)
or
⇒ 5120 – 3840 < 6x – 2x
⇒ 4x > 1280 or x > 320 ... (2)
From (1) and (2), we have 320 < x < 1280
Thus, the number of litres to be added, should be greater than 320 litres and less than 1280 litres.
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