A milk of 80% concentration is diluted at home by the seller by adding some water to it so that milk concentration is reduced between 65% to 70%. If 640 litres of milk of 80% concentration is available, how much water has been added? Which value system the seller is lacking.

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Amount of milk in 80% concentrated milk mixture of 640 litres is = 0.8 *640=512 litres.

Let X litres of milk be added to the 80% milk mixture to to get concentration between 65% and 70%.
Amount of milk in  65% milk mixture =  (65/100 )* (640+X) litres.
Amount of milk in  70% milk mixture =  (70/100 )* (640+X) litres
 
(65/100)* (640+X) < 512 < 70/100(640+X)
   
 => 0.65(640+X) < 512 < 0.70(640+X)
=>  416 + 0.65 X < 512 < 448 + 0.70 X 

=>  512 > 416 + 0.65 X and 448+ 0.70X > 512
=>  96 > 0.65 X  and  0.7 X > 64
=>  X < 96/0.65 and  X > 64/0.7
=>  X < 147.69  and X > 91.43 





 
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Above solution, it is X litres of water to be added, not milk. . Apologies for confusion.
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