Question

The denominator of a rational number is greater than its numerator by 2. If 1 is added to numerator and denominator increased by 3, the number obtained is 1 /2 . Find the rational number.

Answer 1

Given :

• Denominator of a rational number is greater than its numerator by 2.
• If 1 is added to numerator and denominator is increased by 3, the number obtained is 1 /2 .

To Find :

• Rational Number

Solution :

$\longmapsto\tt{Let\:the\:numerator\:be=x}$

• As Given that Denominator is greater than its numerator by 2. So ,

$\longmapsto\tt{Denominator=x+2}$

Now ,

• If 1 is added to numerator and denominator is increased by 3, the number obtained is 1 /2 .

$\longmapsto\tt{Numerator=x+1}$

$\longmapsto\tt{Denominator=x+2+3}$

$\longmapsto\tt{x+5}$

A.T.Q :

$\longmapsto\tt{\dfrac{x+1}{x+5}=\dfrac{1}{2}}$

$\longmapsto\tt{2(x+1)=1(x+5)}$

$\longmapsto\tt{2x+2=1x+5}$

$\longmapsto\tt{2x-1x=5-2}$

$\longmapsto\tt{1x=3}$

$\longmapsto\tt\bold{x=3}$

Therefore :

$\longmapsto\tt{Numerator=x}$

$\longmapsto\tt\bold{3}$

$\longmapsto\tt{Denominator=3+2}$

$\longmapsto\tt\bold{5}$

So , The number is 3/5...