Question

The denominator of a fraction is 2 more than the numerator. If 1 is substracted from the numerator and 1 is added to the denominator , the fraction becomes 1/2. What is that fraction?​

Answer 1

Denominator is 2 more than the numerator.

$\tt{Fraction \to \dfrac{x}{x+2}}$

According to the Question,

• 1 is subtracted from numerator
• 1 is added to the denominator

The fraction becomes 1/2

$\\\sf{\dfrac{x-1}{x+2+1}=\dfrac{1}{2}}$

$\implies \: \sf{\dfrac{x-1}{x+3}=\dfrac{1}{2}}$

$\implies \: \sf{2(x-1)=x+3}$

$\implies \: \sf{2x-2=x+3}$

$\implies \: \sf{2x-x=3+2}$

$\therefore \: \bf{x=5}$

$\bf{\underline{For \: finding \: the \: fraction,}}$

$\sf{Fraction \to \dfrac{x}{x+2}=\dfrac{5}{5+2}=\dfrac{5}{7}}$

∴ The fraction is 5/7

★ Verification:

Denominator is 2 more than the numerator. 7 is 2 more than 5. So, one part of the answer is correct. ☑

For the second part, subtract 1 from numerator and add 1 to denominator.

The fraction becomes 4/8 which is equal to 1/2 as per the Question.

So the answer is fully correct ☑