Question

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

Answer 1

Step-by-step explanation:

Let the numerator and denominator of the fraction be x and y respectively. Then,

Fraction = x/y

It is given that

Denominator =2 (Numerator) +4

⇒y=2x+4

⇒2x−y+4=0

According to the given condition, we have

y−6=12(x−6)

⇒y−6=12x−72

⇒12x−y−66=0

Thus, we have the following system of equations

2x−y+4=0 .(i)

12x−y−66=0 ..(ii)

Subtracting equation (i) from equation (ii), we get

10x−70=0

⇒x=7

Putting x=7 in equation (i), we get

14−y+4=0

⇒y=18

Hence, required fraction = 7/18

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Answer 2

⠀⠀⠀⠀⠀☯ Let the Numerator and the denominator of the fraction be

x and y respectively.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore,

The fraction become = $\sf \dfrac{x}{y}$

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

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

$:\implies\sf 2x - y + 4 = 0\qquad\qquad\bigg\lgroup\bf eq\;(1) \bigg\rgroup$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\quad\qquad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: According\: to \:given \: condition :}}}}}\mid}$

When both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator.

$:\implies\sf y - 6 = 12(x - 6)$

$:\implies\sf y - 6 = 12x - 72$

$:\implies\sf 12x - y - 66 = 0\qquad\qquad\bigg\lgroup\bf eq\;(2) \bigg\rgroup$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

☯ Now, Subtracting eq (1) from eq (ii),

$:\implies\sf 10x - 70 = 0$

$:\implies\sf 10x = 70$

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

$:\implies{\boxed{\frak{\pink{x = 7}}}}\;\bigstar$

☯ Now, Putting value of x in eq (1),

$:\implies\sf 14 - y + 4 = 0$

$:\implies\sf - y + 18 = 0$

$:\implies{\boxed{\frak{\pink{y = 18}}}}\;\bigstar$

$\therefore$ Hence, required fraction is $\bf \dfrac{7}{18}$.