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

  • question_answer
    The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes \[\frac{1}{5}\]. Then the original number was ____.

    A)  \[\frac{7}{11}\]                     

    B)  \[\frac{3}{5}\]           

    C)  \[\frac{5}{8}\]                       

    D)         \[\frac{4}{7}\]           

    Correct Answer: C

    Solution :

    Let the number be \[\frac{x}{y}\] According to the question,                      \[y=x+3\] \[\Rightarrow \]  \[x=y-3\]                .....(1) Also, \[\frac{x-3}{y+2}=\frac{1}{5}\]  \[\Rightarrow \]  \[5x-15=y+2\] \[\Rightarrow \]            \[5x=y+17\]                ??(2) Solving (1) and (2), we get \[x=5\]and \[y=8~\] \[\therefore \]  Required number \[=\frac{x}{y}=\frac{5}{8}\]


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