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Discussion :: Alligation or Mixture

  1. A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

    2. A.

    \(\frac { 1 } {3 }\)
    B.

    \(\frac { 1 } {4 }\)
    C.

    \(\frac { 1 } {5 }\)
    D.

    \(\frac { 1 } {7 }\)

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    Answer : Option C

    Explanation :

    Suppose the vessel initially contains 8 litres of liquid.

    Let x litres of this liquid be replaced with water.

    Quantity of water in new mixture =[ 3- \(\frac { 3X } { 8 } \) +x]litres

    Quantity of syrup in new mixture =[5 - \(\frac { 5X } { 8 } \)]litres

    [3- \(\frac { 3X } { 8 } \)+x] =[ 5-\(\frac { 5X } { 8 } \)]

     5x + 24 = 40 - 5x

     10x = 16

     x =\(\frac {8 } {5 } \)

    So, part of the mixture replaced = [\(\frac {8 } {5 } \)x \(\frac {1 } {8 } \)]=\(\frac {1 } {5 } \)

     

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