NCERT Class XI Mathematics - Linear Inequalities - Solutions
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Question : 64
Total: 65
How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
Solution:
Let x litre water is added to 45% solution of acid.
(i) 25 % of (1125 + x) <
⇒ 5(1125 + x) < 10125 ⇒ 5625 + 5x < 10125 ⇒ 5x < 10125 – 5625
or x <
(ii) Further, 30% of (1125 + x) >
or
⇒ 6(1125 + x) > 1125 × 9 ⇒ 6750 + 6x > 10125
⇒ 6x > 10125 – 6750 ⇒ 6x > 3375
or x >
From (1) and (2), we have 562.5 < x < 900
(i) 25 % of (1125 + x) <
⇒ 5(1125 + x) < 10125 ⇒ 5625 + 5x < 10125 ⇒ 5x < 10125 – 5625
or x <
(ii) Further, 30% of (1125 + x) >
or
⇒ 6(1125 + x) > 1125 × 9 ⇒ 6750 + 6x > 10125
⇒ 6x > 10125 – 6750 ⇒ 6x > 3375
or x >
From (1) and (2), we have 562.5 < x < 900
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