Question

Sum of numerator and denominator of a fraction is 4 more than double its numerator.
If 1 is added to the numerator then ratio of numerator and denominator becomes 2 : 3. Find the
fraction.​

Answer 1

Answer :

The required fraction is 5/9

Given :

• Sum of the numerator and denominator of a fraction is 4 more than double its numerator .
• If 1 is added to the numerator then ratio of numerator and denominator becomes 2:3

To Find :

• The fraction

Solution :

Let us consider the numerator be x and denominator be y

According to question :

$\sf \implies x + y = 4 + 2x \\\\ \sf \implies x + y - 2x = 4 \\\\ \sf \implies y - x = 4 \\\\ \sf \implies y = 4+x..........(1)$

Again by question :

$\sf \implies \dfrac{x+1}{y} = \dfrac{2}{3} \\\\ \sf \implies 3(x + 1) = 2y \\\\ \sf \dagger Putting \: \: the \: \: value \: \: of \: \: y \: \: from (1) \\ \sf in \: \: the \: \: above \:\: equation \\\\ \sf \implies 3(x + 1) = 2(4+x) \\\\ \sf \implies 3x + 3 = 8 + 2x \\\\ \sf \implies 3x - 2x = 8 - 3 \\\\ \sf \implies x = 5$

Now using the value of x in (1) :

$\sf \implies y = 4 + 5 \\\\ \sf \implies y = 9$

Thus the required fraction is :

$\sf \longrightarrow \dfrac{5}{9}$

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the numerator be x.

And the denominator be y.

Fraction = x/y.

According to the Question,

1st part,

⇒ x + y = 4 + 2x

⇒ x + y = 4

⇒ x = y - 4 ... (i)

2nd part,

⇒ x + 3/y + 3 = 2/3

By cross-multiplying both sides, we get

⇒ 3x + 9 = 2y + 6

⇒ 3x - 2y = - 3 .... (ii)

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

⇒ 3x - 2y = - 3

⇒ 3(y - 4) - 2y = - 3

⇒ 3y - 12 - 2y = - 3

⇒ y - 12 = - 3

⇒ y = - 3 + 12

⇒ y = 9

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

⇒ x = y - 4

⇒ x = 9 - 4

⇒ x = 5

Fraction = x/y = 5/9

Hence, the required fraction is 5/9.