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31.

729 mL of a mixture contains milk and water in the ratio 7 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7 : 3?

  • 52 mL

  • 60 mL

  • 71 mL

  • 81 mL


D.

81 mL

Quantity of mixture  =  729 mL,   Milk : Water = 7 : 2
   Quantity of milk:
           space equals space fraction numerator 7 over denominator 7 plus 2 end fraction space cross times space 729 space equals space 7 over 9 space cross times space 729 space equals space 567 space mL
∴  Water = 729 - 567 = 162 mL
Let x water be added for new mixture:
 rightwards double arrow space space space fraction numerator 567 over denominator 162 plus straight x end fraction space equals space 7 over 3 space space
rightwards double arrow space space 81 space cross times space 3 space equals space 162 space plus space straight x
rightwards double arrow space space space 243 space equals space 162 space plus space straight x
rightwards double arrow space space space straight x space equals space 243 space minus space 162 space equals space 81 space mL space space
∴  Quantity of water to be added = 81 mL

          


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