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Question:
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?
Answer:

Let amount of water is added = x litre

Given solution is 1125 litre

Percentage of acid in solution = 45%

So percentage of water in solution = 55%

Case 1. Resulting mixture will contain more than 25% acid

      x + 1125*55% = (x + 1125)*75%

=> x + (1125*55)/100 =(x + 1125)*75/100

=> 100x + 1125*55 =(x + 1125)*75

=> 100x + 1125*55 = 75x + 1125*75

=> 100x - 75x = 1125*75 - 1125*55

=> 25x = 1125*(75-55)

=> 25x = 1125*20

=> x = (1125*20)/25

=> x = (1125*4)/5

=> x = 225*4

=> x = 900

Case 2. Resulting mixture will contain more than 30% acid

      x + 1125*55% = (x + 1125)*7%

=> x + (1125*55)/100 =(x + 1125)*70/100

=> 100x + 1125*55 =(x + 1125)*70

=> 100x + 1125*55 = 70x + 1125*70

=> 100x - 70x = 1125*70 - 1125*55

=> 30x = 1125*(70-55)

=> 30x = 1125*15

=> x = (1125*15)/30

=> x = (1125*5)/10

=> x = (1125)/2

=> x = 562.5

So water is added between 562.5 litre to 900 litre  

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