Question

the denominator of the fraction is 5 more than its numerator. if 2is subtracted from both the numerator and the denominator the fraction becomes4/5 find the fraction​

Answer 1

Answer :-

$\large \bold{Given \: That}$

The denominator of the fraction is 5 more than its numerator. if 2is subtracted from both the numerator and the denominator the fraction becomes 4/5.

$\large \bold{To \: Find}$

Find the fraction.

$\large \bold{Solution}$

Let the Numerator be 'x'.

and, Denominator be '5x'.

According to question.

$= > \: \: \frac{x \: - \: 2}{5x \: - \: 2} \: \: = \: \: \frac{4}{5} \\ \\ = > \: \: 5 \: (x \: - \: 2) \: \: = \: \: 4 \: (5x \: - \: 2) \\ \\ = > 5x \: - \: 10 \: \: = \: \: 20x \: - \: 8 \\ \\ = > \: \: - 10 \: + \: 8 \: \: = \: \: 20x \: - \: 5x \\ \\ = > - 2 \: \: = \: \: 15x \\ \\ = > \: \: x \: \: = \: \: \frac{ - 2}{15}$

Thanks My Answer

Answer 2

Answer:

$\sf{The \: fraction \: is \: \: \dfrac{22}{27}}$

Step-by-step explanation:

Let,

The numerator of the fraction = x

The denominator of the fraction = x + 5

★ If 2 is subtracted from both the numerator and the denominator

The numerator of the fraction = x - 2

The denominator of the fraction = x + 5 - 2

⇒ x + 5 - 2

⇒ x + 3

.°. The denominator of the fraction = x + 3

⇒ $\sf{\dfrac{x \: - \: 2}{x \: + \: 3} \: = \: \dfrac{4}{5}}$

⇒ 5 (x - 2) = 4 (x + 3)

⇒ 5x - 10 = 4x + 12

⇒ 5x - 4x = 12 + 10

⇒ 1x = 22

⇒ x = 22

The numerator of the fraction = 22

The denominator of the fraction = x + 5

⇒ 22 + 5

⇒ 27

The denominator of the fraction = 27

Therefore,

$\sf{The \: fraction \: is \: \: \dfrac{22}{27}}$