Question

The denominator of a fraction is 3 more than numerator. if 2 is added to the denominator the fraction becomes 1/2. find the original fraction. give explanation ​

Answer 1

Answer :-

• The fraction is 5/8.

Given :-

• The denominator of a fraction is 3 more than numerator. if 2 is added to the denominator the fraction becomes 1/2.

To Find :-

• Original fraction.

Solution :-

→ Let numerator be x

→ Denominator is 3 more than the numerator = x + 3

→ 2 is added to the denominator = x + 3 + 2 = x + 5

→ New fraction = 1/2

According to question :-

⇒ x/x+5 = 1/2

⇒ 2 × x = x + 5

⇒ 2x = x + 5

⇒ 2x - x = 5

⇒ x = 5

Now

• Numerator = x = 5
• Denominator = x + 3 = 5 + 3 = 8

Hence, the fraction is 5/8.

Answer 2

Given :

• The denominator of a fraction is 3 more than numerator. if 2 is added to the denominator the fraction becomes 1/2 .

To Find :

• The original fraction

Solution :

• Let us assume the numerator to be 'a' .

• According To The Question :

Denominator = a + 3

Now , if 2 is added to denominator it would become 1/2 .

i.e. Denominator = a + 3 + 2 = a + 5

• On Solving :

$\implies \sf \dfrac{a}{a\:+\:5} \:=\: \dfrac{1}{2}$

$\implies \sf 2a\:=\:a\:+\:5$

$\implies \sf 2a\:-\:a\:=\:5$

$\implies \sf a\:=\: 5$

• Therefore , the numerator is 5 and the denominator is 3 more than 5 i.e. 8 .

$\large\bold{\boxed{\sf{Fraction\:=\: \dfrac{5}{8}}}}$

_________________________