A fraction becomes 1/2, when 1 is subtracted from the numerator and it becomes 1/4 ,when 8 is added to its denominator.Find the f

2 thoughts on “A fraction becomes 1/2, when 1 is subtracted from the numerator and it becomes 1/4 ,when 8 is added to its denominator.Find the f”

1. Answer:

   The value of Fraction is [tex]\frac{3}{4}[/tex].

   Step-by-step explanation:

   Let us assume Numerator as= x

   Let us assume Denominator as= y

   According to the question the first equation is

   ⇒[tex]\frac{x-1}{y} =\frac{1}{2}[/tex]

   ⇒[tex]2(x-1)=y(1)[/tex]

   ⇒[tex]2x-2=y[/tex]

   ⇒[tex]2x-y=2[/tex] —1st equation

   According to the question the Second equation is

   ⇒[tex]\frac{x}{y+8} =\frac{1}{4}[/tex]

   ⇒[tex]4(x)=(y+8)1[/tex]

   ⇒[tex]4x=y+8[/tex]

   ⇒[tex]4x-y=8[/tex]—2nd equation

   Solve equation one and two

   [tex](4x-y=8)-(2x-y=2)[/tex]

   The result is [tex]2x=6[/tex]

   ⇒[tex]x=\frac{6}{2}[/tex]

   ⇒[tex]x=3[/tex]

   Substitute x value in 1st equation

   ⇒[tex]2(3)-y=2[/tex]

   ⇒-[tex]y=2-6[/tex]

   ⇒[tex]y=4[/tex]

   The value of Numerator is 3.

   The value of denominator is 4.

   The value of Fraction is [tex]\frac{3}{4}[/tex].

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2. Let the fraction be,

   [tex]\frac{x}{y}\\\\\\[/tex]

   Now,

   [tex]{{\frac{x-1}{y} =\frac{1}{2}} \\\\\ \: \: and \: \: {\frac{x}{y+8}=\frac{1}{4} }} \right. \\\\\frac{x-1}{y} = \frac{1}{2}\\\\2x – 2=y \: \: \: \: \\2x-y =2 .. (1)\\\\\frac{x}{y+8}=\frac{1}{4}\\\\4x= y+8\: \: \: \: \\4x-y=8 .. (2)\\\\\\\\\\Subtracting\: (1) from (2)\\\\(1)\: \: 2x – y=2 \\-\:\: \: 4x-y=8\\= -2x=-6\\x=\frac{-6}{-2} \\x=3\\\\and,\: 4x= y+8\\\:\:\:\:\: 4\times 3=y+8\\y=12-8=4\\\\[/tex]

   [tex]Hence, \: \frac{x}{y} =\frac{3}{4}[/tex]

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