The sum of numerator and denominator of a fraction is greater by 1
than thrice the numerator. If the numerator is decreased b

2 thoughts on “The sum of numerator and denominator of a fraction is greater by 1<br />than thrice the numerator. If the numerator is decreased b”

1. [tex]\huge{\textbf{\textsf{{\orange{A}}{\blue{n}}{\pink{s}}{\purple{w}}{\red{e}}{\green{r}}{\color{gold}{: }}{\color{navy}{-}}}}}[/tex]

   Given :-

   Sum of numerator and denominator of a fraction is greater by 1

   than thrice the numerator. If the numerator is decreased by 1 then the

   fraction reduces to 1/3

   To Find :-

   Fraction

   Solution :-

   Let the fraction be x/y

   [tex]\sf x + y = 3(x)+1[/tex]

   [tex]\sf x + y = 3x+1[/tex]

   [tex]\sf 0-1 = 3x-x-y[/tex]

   [tex]\sf -1 = 2x -y[/tex]

   [tex]\sf y = 2x+1[/tex]

   Now

   When decreased by 1

   [tex]\sf\dfrac{x-1}{y} =\dfrac{1}{3}[/tex]

   By cross multiplication

   (y) = 3(x – 1)

   y = 3x – 3

   y = 3x – 3

   Substituting the value of y

   [tex]\sf 3x – 2x-1=3[/tex]

   [tex]\sf x-1=3[/tex]

   [tex]\sf x =3+1[/tex]

   [tex]\sf x =4[/tex]

   Finding the numerator

   [tex]\sf y = 3(4) – 3[/tex]

   [tex]\sf y = 12-3[/tex]

   [tex]\sf y =9[/tex]

   [tex]\bf Fraction = \dfrac{x}{y}[/tex]

   [tex]\sf Fraction = \dfrac{4}{9}[/tex]

   Reply

2. Given :-

   Sum of numerator and denominator of a fraction is greater by 1

   than thrice the numerator. If the numerator is decreased by 1 then the

   fraction reduces to 1/3

   To Find :-

   Fraction

   Solution :-

   Let the fraction be x/y

   [tex]\sf x + y = 3(x)+1[/tex]

   [tex]\sf x + y = 3x+1[/tex]

   [tex]\sf 0-1 = 3x-x-y[/tex]

   [tex]\sf -1 = 2x -y[/tex]

   [tex]\sf y = 2x+1[/tex]

   Now

   When decreased by 1

   [tex]\sf\dfrac{x-1}{y} =\dfrac{1}{3}[/tex]

   By cross multiplication

   (y) = 3(x – 1)

   y = 3x – 3

   y = 3x – 3

   Substituting the value of y

   [tex]\sf 3x – 2x-1=3[/tex]

   [tex]\sf x-1=3[/tex]

   [tex]\sf x =3+1[/tex]

   [tex]\sf x =4[/tex]

   Finding the numerator

   [tex]\sf y = 3(4) – 3[/tex]

   [tex]\sf y = 12-3[/tex]

   [tex]\sf y =9[/tex]

   [tex]\bf Fraction = \dfrac{x}{y}[/tex]

   [tex]\sf Fraction = \dfrac{4}{9}[/tex]

   Reply