Question

the denominator of a fraction is 4more than it twice the number when the numerator and denominator are decreased by 6 then denominator become 12time of number determine the fraction​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:The\:fraction\:=\:\dfrac{7}{18}}}}$

Step-by-step-explanation:

Let the numerator of the fraction be x.

And the denominator of the fraction be y.

$\displaystyle{\sf\therefore\:The\:fraction\:=\:\dfrac{x}{y}}$

From the first condition,

y = 2x + 4 $\qquad$ - - - ( 1 )

From the second condition,

( y - 6 ) = 12 ( x - 6 )

⇒ ( 2x + 4 - 6 ) = 12x - 72

⇒ 2x - 2 = 12x - 72

⇒ - 2 + 72 = 12x - 2x

⇒ 10x = 70

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{70}{10}}}$

$\displaystyle{\implies\boxed{\blue{\sf\:x\:=\:7\:}}}$

By substituting x = 7 in equation ( 1 ), we get,

y = 2x + 4 $\qquad$ - - - ( 1 )

⇒ y = 2 * 7 + 4

⇒ y = 14 + 4

$\displaystyle{\implies\boxed{\pink{\sf\:y\:=\:18}}}$

Now,

$\displaystyle{\sf\:The\:fraction\:=\:\dfrac{x}{y}}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:The\:fraction\:=\:\dfrac{7}{18}}}}}$

Answer 2

Let the numerator of the fraction be x.

And the denominator of the fraction be y.

$\large \tt the \: \: fraction \: \: = \frac{x}{y}$

From the first condition,

y = 2x + 4 ____ ( 1 )

From the second condition,

( y - 6 ) = 12 ( x - 6 )

⇒ ( 2x + 4 - 6 ) = 12x - 72

⇒ 2x - 2 = 12x - 72

⇒ - 2 + 72 = 12x - 2x

⇒ 10x = 70

⇒ x = 7

By substituting x = 7 in equation ( 1 ), we get,

y = 2x + 4 _____( 1 )

⇒ y = 2 * 7 + 4

⇒ y = 14 + 4

⇒ y = 18

$\Large \tt \green\ddag \: \: The \: \: \: Fraction \: \: is \: \: \: \color{orange} \frac{7}{18}$