Question

10.The denominator of a fraction is 4 more than its numerator. If the numerator is

increased by 2 and the denominator is increased by 5, the fraction obtained is 5/12.

Find the fraction.
pls give the answer step by step​

Answer 1

Answer:

Let the numerator be x .

so, denominator = x + 4

if ,

numerator = x + 2

and, denominator = x + 4 + 5 = x + 9

so, fraction = \frac{5}{12}

12

5

\textbf{According to the Question,}According to the Question,

\frac{x + 2}{x + 9} = {\frac{5}{12}}

x+9

x+2

=

12

5

solve by cross multiplication,

$$\begin{lgathered}= > 12(x + 2) = 5(x + 9) \\ \\ = > 12x + 24 = 5x + 45\end{lgathered}$$

take the like terms to one side :-

$$\begin{lgathered}= > 12x - 5x = 45 - 24 \\ \\ = > 7x = 21 \\ \\ = > x = \frac{21}{7} \\ \\ = > x = 3\end{lgathered}$$

thus ,

numerator = x = 3

and, denominator = x + 4 = 3 + 4 = 7

hence, fraction = $$\frac{3}{7}$$ .

Step-by-step explanation:

HOPE IT WILL HELP YOU DEAR......

PLZ FOLLOW ME......

AND MARK MY ANSWER IF IT HELPS YOU......

Answer 2

Answer:

$\sf{The \: fraction \: is \: \: \dfrac{3}{7}}$

Step-by-step explanation:

Let,

The numerator of a fraction = x

The denominator of a fraction = x + 4

If the numerator is increased by 2

⇒ x + 2

The denominator is increased by 5

⇒ x + 4 + 5

⇒ x + 9

⇒ $\sf{\dfrac{x \: + \: 2}{x \: + \: 9} \: \: = \: \: \dfrac{5}{12}}$

⇒ 12 (x + 2) = 5 (x + 9)

⇒ 12x + 24 = 5x + 45

⇒ 12x - 5x = 45 - 24

⇒ 7x = 21

⇒ x = 21 / 7

⇒ x = 3

★ The numerator of a fraction = 3

The denominator of a fraction = x + 4

⇒ x + 4

⇒ 3 + 4

⇒ 7

★ The denominator of a fraction = 7

Therefore,

$\sf{The \: fraction \: is \: \: \dfrac{3}{7}}$