Question

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 fraction

Answer 1

Answer:

The value of Fraction is $\frac{3}{4}$.

Step-by-step explanation:

Let us assume Numerator as= x

Let us assume Denominator as= y

According to the question the first equation is

⇒$\frac{x-1}{y} =\frac{1}{2}$

⇒$2(x-1)=y(1)$

⇒$2x-2=y$

⇒$2x-y=2$ ---1st equation

According to the question the Second equation is

⇒$\frac{x}{y+8} =\frac{1}{4}$

⇒$4(x)=(y+8)1$

⇒$4x=y+8$

⇒$4x-y=8$---2nd equation

Solve equation one and two

$(4x-y=8)-(2x-y=2)$

The result is $2x=6$

⇒$x=\frac{6}{2}$

⇒$x=3$

Substitute x value in 1st equation

⇒$2(3)-y=2$

⇒-$y=2-6$

⇒$y=4$

The value of Numerator is 3.

The value of denominator is 4.

The value of Fraction is $\frac{3}{4}$.

Answer 2

Let the fraction be,

$\frac{x}{y}$

Now,

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

$Hence, \: \frac{x}{y} =\frac{3}{4}$