Mathematics85 kg of a mixture contains milk and water in the ratio 27:7. How much  more water is to be added to get a new mixture containing milk and  water in the ratio 3:1? Chapter/Topic:   Comparing quantities

85 kg of a mixture contains milk and water in the ratio 27:7. How much  more water is to be added to get a new mixture containing milk and  water in the ratio 3:1?
 


Chapter/Topic:   Comparing quantities


  1. A
    5kg
  2. B
    6.5kg
  3. C
    7.25kg
  4. D
    8kg 

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    Solution:

    Total mixture= 85 kg,
     let:  m = amount of milk 
    85 - m = amount of water. 
    Ratio = 27:7 (milk:water),
    27/7m/(85-m)
    27Solve for m using cross-multiplication: 
    27(85−m)=7m
    2295−27m=7m
    2295=34m
    m=135/2
    135/2 kg milk, which means that we have: 
    water=85 - 135/2 
              =170/2 - 135/2 
              =35/2 kg water 
     water to be added to make the ratio 3:1. 
    Let n = amount of water added. 
    3/1=(135/2)/(35/2+n)    
    Now, solve for n.

    Again, start with cross multiplication: 
    3(35/2+n)=135/2
    105/2+3n=135/2
    3n=30/2
    n = 5
    Hence, 5 kg water is to be added to get a new mixture containing milk and  water in the ratio 3:1.
    Hence, Option (1) is the correct answer.
      
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