Question

The denominator of a fraction is 4 more than
twice the numerator. When both the numera-
tor and denominator are decreased by 6, then
the denominator becomes 12 times the nu-
merator. Then the fraction is :


​

Answer 1

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

Fraction = x/y

Denominator = 2(Numerator) + 4

- y = 2x + 4

- 2x - y + 4 = 0

According to the condition,

- y - 6 = 12(x - 6)

- y - 6 = 12x 72

- 12x y 66 = 0

Here, we have the following system of equations

2x - y +4= 0. (i)

12x - y 66 = 0.(ii)

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

- 10x - 70 = 0

- x=7

Putting x's value in eq (i), we get

14 - y +4 = 0

- y= 18

Hence, the fraction is 7/18.

Answer 2

Answer:

The fraction is 7/18

Step-by-step explanation:

Let,

The Numerator of fraction = x

The Denominator of a fraction is 4 more than twice the Numerator :

The Denominator of fraction = 2x + 4

Fraction = x/2x + 4

When both the Numerator and Denominator are decreased by 6 :

The Numerator = x - 6

The Denominator = 2x + 4 - 6 = 2x - 2

Then, the Denominator becomes 12 times the Numerator

★ According to the Question :

⇒ 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

⇒ 14 + 4

⇒ 18

The Denominator of fraction = 18

The fraction = 7/18

∴ The fraction is 7/18