Question

the denominator of fraction is 4 more than twice the numerator. when both numerator and denominator are decreased by 6 then the denominator becomes 12 times the numerator . find the fraction​

Answer 1

Answer:

Step-by-step explanation:

Given :-

The denominator of a fraction is 4 more than twice its numerator.

Denominator becomes 12 times the numerator ,if both the numerator and denominator are reduced by 6.

To Find :-

The Fraction.

Solution :-

Let the numerator be x.

And the denominator be (2x + 4)

Fraction = x/(2x + 4)

⇒ 12(x - 6) = (2x + 4 - 6)

⇒ 12x - 72 = 2x - 2

⇒ 12x - 2x = -2 + 72

⇒ 10x = 70

⇒ x = 70/10

⇒ x = 7

Numerator = x = 7

Denominator = 2x + 4 = 2 × 7 + 4) = (14 + 4) = 18

Hence, The Fraction is 7/18.

Answer 2

Given :

• The denominator of fraction is 4 more than twice the numerator.
• When both numerator and denominator are decreased by 6 then the denominator becomes 12 times the numerator.

To Find :

• The fraction.

Solution :

Let the numerator of the fraction be x.

Let the denominator of the fraction be y.

Fraction → $\sf{\dfrac{x}{y}}$

Case 1 :

Denominator = 2 × Numerator + 4

Equation :

$\sf{y=2x+4}$___(1)

Case 2 :

Numerator → (x -6)

Denominator → ( y - 6)

Equation :

$\longrightarrow$ $\sf{(y-6)=12(x-6) }$

$\longrightarrow$ $\sf{(y-6) = 12x-72}$

$\longrightarrow$ $\sf{y-6=12x-72}$

$\longrightarrow$ $\sf{y=12x-72+6}$

$\longrightarrow$ $\sf{y=12x-66}$

From (1), y = 2x + 4,

$\longrightarrow$ $\sf{2x+4=12x-66}$

$\longrightarrow$ $\sf{2x-12x=-66-4}$

$\longrightarrow$ $\sf{-10x=-70}$

$\longrightarrow$ $\sf{10x=70}$

$\longrightarrow$ $\sf{x\:=\cancel\dfrac{70\:^7}{10\:^1}}$

$\longrightarrow$ $\sf{x=7}$

Substitute, x = 7 in equation (1),

$\longrightarrow$ $\sf{y=2x+4}$

$\longrightarrow$ $\sf{y=2(7)+4}$

$\longrightarrow$ $\sf{y=14+4}$

$\longrightarrow$ $\sf{y=18}$

Fraction :

$\large{\boxed{\sf{\red{Numerator\:=\:x\:=\:7}}}}$

$\large{\boxed{\sf{\purple{Denominator\:=\:y\:=\:18}}}}$

$\large{\boxed{\sf{\blue{Fraction\:=\:\dfrac{x}{y}\:=\:\dfrac{7}{18}}}}}$