Question

(m) The denominator of a fraction is 4 more than twice its numerator. Denominator
becomes 12 times the numerator, if both the numentor and the denominator
are reduced by 6. Find the fraction​

Answer 1

Answer:

let the numerator be x.

AND denominator be (2x + 4)

fraction is x/(2x + 4)

now,

12(x - 6) = (2x + 4 - 6)

=> 12x - 72 = 2x - 2

=> 12x - 2x = -2 + 72

=> 10x = 70

=> x = 70/10

=> x = 7

AND,

DENOMINATOR be (2×7 + 4) = (14 + 4) = 18

fraction = 7/18

Hope it's helps uhh❤✨

Answer 2

$\bold\red{Sσℓυтíση:}$

$\bold{Let \: the \: fraction \: be \: \frac{x}{y} }$

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

So,

$\bold {y \:= \:4\:+\:2x \:⇒ \:2x \:-4.\: (i) }$

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

So,

$\bold {y\: - \:6 \:= \:12\: (x - 6)}$

⇒y-6 = 12x - 72

⇒12x - y = 72 - 6 = 66

⇒12x y = 66... (ii)

Subtracting (i) from (ii)

⇒12x − 2x − y − (−y) = 66 − (−4).

⇒ 10x = 70

$⇒x = \frac{70}{10} \\ \\ ⇒x = \cancel\frac{70}{10} = 7$

⇒ x = 7

Putting the value of x = 7 in (i)

2 (7) - y = - 4

⇒14 - y = - 4

⇒y = 14 + 4 = 18

$\bold{Thus, \: the \: fraction \: is \: \frac{7}{18} }$

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