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SSC Quantitative Aptitude Mixture And Alligation Question Bank Mixture and Allegation (I)

  • question_answer
    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?

    A) \[\frac{1}{3}\]

    B) \[\frac{1}{4}\]

    C) \[\frac{1}{5}\]

    D) \[\frac{1}{7}\]

    Correct Answer: C

    Solution :

    [c] Let the vessel initially contain 8 L of liquid. Let x L of this liquid be replaced with water. Quantity of water in the new mixture \[=\left( 3-\frac{3x}{8}+x \right)L\] Quantity of syrup in the new mixture \[=\left( 5-\frac{5x}{8} \right)L\] \[\therefore \]            \[3-\frac{3x}{8}+x=5-\frac{5x}{8}\] \[\Rightarrow \]         \[24-3x+8x=40-5x\] \[\Rightarrow \]         \[10x=16\] \[\Rightarrow \]         \[x=\frac{16}{10}=\frac{8}{5}\] Part of the mixture replaced       \[=\left( \frac{1}{8}\,\,\text{of}\,\,\frac{8}{5} \right)=\frac{1}{5}\]


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