Question

the denominator of a fraction is 4 more than twice its numerator if 6 is substrated from both numerator and denominator the denominator becomes 12 times the denominator. find fraction​

Answer 1

To Find:-

Find the fraction.

Given:-

• The denominator of a fraction is 4 more than twice its numerator if 6 is substracted from both numerator and denominator becomes 12 times the denominator.

Solution:-

Let the numerator be " x "

Denominator be " y "

So,

Fraction be $\tt \: \dfrac { x } { 2x + 4 }$

Given,

$\tt\implies \: 12( x - 6 ) = ( 2x + 4 - 6 )$

$\tt\implies \: 12x - 72 = 2x - 2$

$\tt\implies \: 12x - 2x = 72 - 2$

$\tt\implies \: 10x = 70$

$\tt\implies \: \cancel\dfrac { 70 } { 7 }$

$\tt\implies \: x = 7$

Hence,

• Numerator is 7

• Denominator is 2x + 4 = 18

∴ Fraction is $\tt \: \dfrac { 7 } { 18 }$

Answer 2

Given :-

• The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6.

To Find:-

• The fraction.

Solution:-

Let the fraction be $\sf\dfrac{x}{y}$

• Denominator of a fraction is 4 more than twice its numerator. 

➙ y = 4 + 2x

➙ 2x - y = -4 (I)

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

So,

➙ y - 6 = 12 (x - 6)

➙ y - 6 = 12x - 72

➙ 12x - y = 72 - 6

➙ 12x - y = 66 (II)

Subtracting (I) from (II)

➙ 12x - 2x - y - (-y) = 66 - (-4)

➙ 10x = 70

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

➙ x = 7

Putting the value of x - 7 in (I)

➙ 2(7) - y = -4

➙ 14 - y = -4

➙ y = 14 + 4

➙ y = 18

Thus, the fraction is $\sf\dfrac{7}{18}$

Answer:-

$\boxed{★\:\:{\bf{\red{\dfrac{7}{18}}}}}$

★ Hope it helps u ★