Given :

• The denominator of a fraction is twice the numerator .
• When borlth are increased by 2, the fraction become 3/4 .

To Find :

• Fraction .

Solution :

[tex]\longmapsto\tt{Let\:Numerator\:be=x}[/tex]

As Given that the denominator is twice the numerator . So ,

[tex]\longmapsto\tt{Denominator=2x}[/tex]

• If both are increased by by 2, the fraction become 3/4 .

[tex]\longmapsto\tt{Numerator=x+2}[/tex]

[tex]\longmapsto\tt{Denominator=2x+2}[/tex]

A.T.Q :

[tex]\longmapsto\tt{\dfrac{x+2}{2x+2}=\dfrac{3}{4}}[/tex]

[tex]\longmapsto\tt{4(x+2)=3(2x+2)}[/tex]

[tex]\longmapsto\tt{4x+8=6x+6}[/tex]

[tex]\longmapsto\tt{4x-6x=6-8}[/tex]

[tex]\longmapsto\tt{-2x=-2}[/tex]

[tex]\longmapsto\tt\bf{x=1}[/tex]

Value of x is 1 .

Therefore :

[tex]\longmapsto\tt{Numerator=x}[/tex]

[tex]\longmapsto\tt\bf{1}[/tex]

[tex]\longmapsto\tt{Denominator=2(1)}[/tex]

[tex]\longmapsto\tt\bf{2}[/tex]

So , The Fraction is 1/2 .

Answer:

Correct Question :-

• The denominator of a fraction is twice the numerator. When both are increased by 2, the fraction become 3/4. Find the fraction ?

Given :-

• The denominator of a fraction is twice the numerator.
• When both are increased by 2, the fraction becomes 3/4.

To Find :-

• What is the fraction.

Solution :-

Let,

[tex]\mapsto \bf Numerator =\: y\\[/tex]

[tex]\bigstar[/tex] The denominator of a fraction is twice the numerator.

[tex]\mapsto \bf Denominator =\: 2y\\[/tex]

So, the required fraction become :

[tex]\leadsto \sf Fraction =\: \dfrac{Numerator}{Denominator}\\[/tex]

[tex]\leadsto \sf\bold{Fraction =\: \dfrac{y}{2y}}\\[/tex]

❒ According to the question :

[tex]\bigstar[/tex] When both are increased by 2, the fraction become 3/4.

So,

[tex]\implies \sf\boxed{\bold{\bigg\{\dfrac{Numerator + 2}{Denominator + 2}\bigg\} =\: \bigg\{\dfrac{3}{4}\bigg\}}}\\[/tex]

[tex]\implies \sf \dfrac{y + 2}{2y + 2} =\: \dfrac{3}{4}\\[/tex]

By doing cross multiplication we get,

[tex]\implies \sf 3(2y + 2) =\: 4(y + 2)\\[/tex]

[tex]\implies \sf 6y + 6 =\: 4y + 8\\[/tex]

[tex]\implies \sf 6y - 4y =\: 8 - 6\\[/tex]

[tex]\implies \sf 2y =\: 2\\[/tex]

[tex]\implies \sf y =\: \dfrac{\cancel{2}}{\cancel{2}}\\[/tex]

[tex]\implies \sf y =\: \dfrac{1}{1}\\[/tex]

[tex]\implies \sf\bold{y =\: 1}\\[/tex]

Hence, the required fraction will be :

[tex]\dag[/tex] Required Fraction :

[tex]\dashrightarrow \sf Required\: Fraction =\: \dfrac{y}{2y}\\[/tex]

[tex]\dashrightarrow \sf Required\: Fraction =\: \dfrac{1}{2(1)}\\[/tex]

[tex]\dashrightarrow \sf Required\: Fraction =\: \dfrac{1}{2 \times 1}\\[/tex]

[tex]\dashrightarrow \sf\bold{\underline{Required\: Fraction =\: \dfrac{1}{2}}}\\[/tex]

[tex]\small \sf\boxed{\bold{\therefore\: The\: required\: fraction\: is\: \dfrac{1}{2}\: .}}\\[/tex]