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

  • question_answer
    A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 L of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was there in the can initially?

    A) 10 L

    B) 20 L

    C) 21 L

    D) 25 L

    Correct Answer: C

    Solution :

    [c] Initially, let the can hold 7x L and 5x L of A and B, respectively. Quantity of A in remaining mixture \[=\left( 7x-\frac{7}{12}\times 9 \right)\] \[=\left( 7x-\frac{21}{4} \right)\,\,L\] Quantity of B in remaining mixture       \[=\left( 5x-\frac{5}{12}\times 9 \right)=\left( 5x-\frac{15}{4} \right)\,\,L\] According to the question, \[\frac{\left( 7x-\frac{21}{4} \right)}{\left( 5x-\frac{15}{4} \right)+9}=\frac{7}{9}\] \[\Rightarrow \]         \[\frac{28x-21}{20x+21}=\frac{7}{9}\] \[\Rightarrow \]         \[252x-189=140x+147\] \[\Rightarrow \]         \[112x=336\] \[\Rightarrow \]         \[x=3\] Initially the can contained       \[(7\times 3)=21\,L\]


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