Question

1. 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. Find the fraction.​

Answer 1

Solution:-

let the numerator of fraction be x and denominator be y.

By given condition,

y=2x+4---(1)

12(x-6)=y-6

12x-72=y-6

put (1)in it

12x-72=2x+4-6

12x-2x=72+4-6

10x=70

x=7

y=14+4

y=18

fraction=7/18

Answer 2

Answer:

$\sf{The \: fraction \: \: is \: \: \dfrac{7}{18}}$

Explanation:

Let,

The numerator of fraction = x

The denominator of fraction = 2x + 4

$\sf{Fraction = \: \dfrac{x}{2x \: + \: 4}}$

When both the numerator and denominator are decreased by 6 :

The numerator of fraction = x - 6

The denominator of fraction = 2x + 4 - 6

⇒ 2x - 2

The denominator becomes 12 times the numerator :

So,

⇒ 12 (x - 6) = 2x - 2

⇒ 12x - 72 = 2x - 2

⇒ 12x - 2x = - 2 + 72

⇒ 10x = 70

⇒ x = 70 / 10

⇒ x = 7

The numerator of fraction = 7

The denominator of fraction = 2x + 4

⇒ 2 (7) + 4

⇒ 2 × 7 + 4

⇒ 14 + 4

⇒ 18

The denominator of fraction = 18

Therefore,

$\sf{The \: fraction \: \: is \: \: \dfrac{7}{18}}$