6th Class Mathematics Arithmetic Question Bank Arithmetic

  • question_answer If the denominator of a fraction is 1 more than thrice its numerator and if the numerator is increased by one and denominator is reduced by two then its value is 0.5. Find the fraction.  

    A)  \[\frac{1}{2}\]                       

    B)           \[\frac{4}{13}\]

    C)  \[\frac{3}{10}\]                     

    D)           \[\frac{2}{7}\]

    Correct Answer: C

    Solution :

        Case I Let the numerator be x then denominator \[=3x+1\] \[\therefore \]    Fraction \[=\frac{x}{3x+1}\] Case II New numerator = x + 1 New denominator \[=3x+1-2\] New fraction \[=\frac{x+1}{3x-1}\] Given \[\frac{x+1}{3x-1}=0.5\] \[\frac{x+1}{3x-1}\,=\frac{5}{10}\] \[\frac{x+1}{3x-1}=\frac{1}{2}\] \[2(x+1)=3x-1\] \[2x+2=3x-1\] \[2x-3x=-1-2\] \[-x=-3\] \[x=3\] \[\therefore \]    Original fraction\[=\frac{3}{3\times 3+1}\,=\frac{3}{10}\]

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