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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
    The sum of the two digits of a two digit number is 9. The number obtained by interchanging the two digits exceeds the given number by 45. Find the number.

    A) 72

    B) 27

    C) 54

    D) 45

    Correct Answer: B

    Solution :

    [b] Let the digits at units and tens place of the number be x and y respectively.                                       
    \[\therefore \]   The number is \[10y+x\]
    Number obtained by interchanging the digits \[=10x+y\]
    According to the question,
    \[x+y=9\]                ...(1)
    and       \[10x+y-(10y+x)=45\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,9x-9y=45\,\,\,\,\,\,\Rightarrow \,\,\,x-y=5\,\]       …..(2)
    On adding eq. (1) and eq. (2). we get
    \[2x=14\Rightarrow x=7\]
    Substituting value of x in eq. (1), we get
    \[y=9-7=2\]
    Hence, the number is \[10(2)+7=27.\]


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