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

  • question_answer
    A mixture contains 80% acid and rest water. Part of the mixture that should be removed and replaced by the same amount of water to make the ratio of acid and water 4 : 3 is

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

    B) \[\frac{3}{7}th\]

    C) \[\frac{2}{3}rd\]

    D) \[\frac{2}{7}th\]

    Correct Answer: D

    Solution :

    [d] In the mixture, acid\[=80%=\frac{4}{5}\] and water \[=20%=\frac{1}{5}\] Let xth part of the mixture be removed and replaced by water. Then,          \[\frac{\frac{4}{5}-\frac{4}{5}x}{\frac{1}{5}-\frac{1}{5}x+x}=\frac{4}{3}\] \[\Rightarrow \]         \[\frac{4-4x}{1-x+5x}=\frac{4}{3}\]      \[\Rightarrow \]\[\frac{4-4x}{1+4x}=\frac{4}{3}\] \[\Rightarrow \]         \[12-12x=4+16x\] \[\Rightarrow \]                     \[8=28x\] \[\Rightarrow \]         \[x=\frac{8}{28}=\frac{2}{7}\text{th}\]


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