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10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

  • question_answer
    A fraction becomes \[\frac{4}{5}\], if 2 is added to both numerator and denominator, if however 4 is subtracted from both numerator and denominator, then the fraction becomes \[\frac{1}{2}\]. The algebraical representation of situation is

    A) \[5x-4y+2=0,x-y=0\]

    B) \[5x-4y+2=0,2x-y-4=0\]

    C) \[x+4y=0,y+2x=0\]

    D) None of the above

    Correct Answer: B

    Solution :

    Let the numerator of the fraction be x and denominator be y.
    Then, the fraction is \[\frac{x}{y}\]. Now, according to condition I, we have
    \[\frac{x+2}{y+2}=\frac{4}{5}\]
    \[\Rightarrow \,\,\,5x+10=4y+8\]
    [cross-multiply both sides]
    \[\Rightarrow \,\,\,\,5x-4y+2=0\]                 ...(i)
    and according to condition II, we have
    \[\frac{x-4}{y-4}=\frac{1}{2}\]
    [cross-multiply both sides]
    \[\Rightarrow \,\,\,2x-8=y-4\]
    \[\Rightarrow \,\,\,\,2x-y-4=0\]                ...(ii)
    Thus, the algebraic representation of given problem is
    \[5x-4y+2=0\]
    and   \[2x-y-4=0\]


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