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 litres of water is required to be added.

Then, total mixture = (1125 + x) litres

It is evident that the amount of acid contained in the resulting mixture is 45% of 1125 litres. This resulting mixture will contain more than 25% but less than 30% acid content.

Therefore, 30% of (1125 + x) > 45% of 1125 and 25% of (1125 + x) < 45% of 1125

30% of (1125 + x) > 45% of 1125

⇒ 30/100 (1125 + x) > 45/100 x 1125

⇒ 30 (1125 + x) > 45 x 1125

⇒ 30 x 1125 + 30x > 45 x 1125

⇒ 30x > 45 x 1125 - 30 x 1125

⇒ 30x > (45 - 30) x 1125

⇒ x > (15 x 1125)/30

⇒ x > 562.5 ....(1)

25% of (1125 + x) < 45% of 1125

⇒ 25/100 (1125 + x) < 45/100 x 1125

⇒ 25(1125 + x) < 45 x 1125

⇒ 25 x 1125 + 25x < 45 x 1125

⇒ 25x < 45 x 1125 - 25 x 1125

⇒ 25x < (45 - 25) x 1125

⇒ x < (20 x 1125)/25

⇒ x < 900 ....(2)

From (1) and (2), we get, 562.5 < x < 900

Thus, the required number of litres of water that is to be added will have to be more than 562.5 litres but less than 900 litres

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NCERT Solutions Class 11 Maths Chapter 6 Exercise ME Question 13

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?

Summary:

Linear inequations situation is given. We have found that the required number of litres of water that is to be added will have to be more than 562.5 litres but less than 900 litres