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8th Class Mathematics Linear Equations in One Variable Question Bank Linear equations in One Variable

  • 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 its denominator, the new number becomes 1/5. The original rational number is;___.

    A)  \[-\frac{5}{8}\]                                 

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

    C)  \[\frac{3}{8}\]                       

    D)         \[-\frac{3}{8}\]

    Correct Answer: B

    Solution :

    Let numerator be x, then denominator is x+3. \[\therefore \] The original rational number\[=\frac{x}{x+3}\] Now, according to question \[\frac{x-3}{x+3+2}=\frac{1}{5}\Rightarrow \frac{x-3}{x+5}=\frac{1}{5}\] On cross multiplying, we get \[5(x-3)=x+5\] \[\Rightarrow 5x-15=x+5\Rightarrow 5x-x=5+15\] \[\Rightarrow 4x=20\Rightarrow x=\frac{20}{4}=5\] Hence, the original rational number is \[\frac{5}{5+3}=\frac{5}{8}\]


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