Question

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 de
reduced by 6. Find the fraction.​

Answer 1

${\pmb{\underline{\sf{ Required \ Solution ... }}}}$

Let the Numerator of the fraction be x

Again, Denominator be (2x + 4)

Equation be like ${\sf{ \dfrac{x}{2x+4} }}$

Now,

If both the numerator and the denominator reduced by 6 as: ${\sf{ \dfrac{x-6}{2x+4-6} }}$

$\\ \circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ \dfrac{x-6}{2x+4-6} = \dfrac{1}{12} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{x-6}{2x-2} = \dfrac{1}{12} }} \\ \\ \\ \colon\implies{\sf{ 12(x-6) = 2x-2 }} \\ \\ \\ \colon\implies{\sf{ 12x - 72 = 2x - 2 }} \\ \\ \\ \colon\implies{\sf{ 12x-2x = -2+72 }} \\ \\ \\ \colon\implies{\sf{ 10x = 70 }} \\ \\ \\ \colon\implies{\sf{ x = \cancel{ \dfrac{70}{10} } }} \\ \\ \\ \colon\implies{\sf{ x = 7 }}$

Hence...

$\\ {\pmb{\underline{\sf\red{ The \ Fraction \ will \ be \ \dfrac{7}{18} . }}}}$

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 reduced by 6 .

To find :

• The fraction.

Solution :

$\sf Let \\ \sf The \: fraction \: will \: be \: \frac{x}{y}$

$\sf Given \: y = 2x + 4$

$\sf 2x - y = -4$

$\sf We , need \: to \: multiply \: the \: equation \\ \sf \: with \: 6$

$\sf \: \;\;\bf{\;\;\red{1st \: method}}$

$\sf \sf 12x - 6y = -24 \\ \sf(y - 6) = 12(x - 6)$

$\sf \: \;\;\bf{\;\;\red{2nd \: method}}$

$\sf12x−y=66$

$\sf subscract \: ( 1 ) \: and \: ( 2 )$

$\sf y = 18 , x = 7$

$\sf Therefore , \: the \: fraction \: is \: \: \frac {7}{18}$