Question

. The numerator of the fraction is 3 less than the denominator. If 1 is added to both its numerator and denominator it becomes 12 . Find the fraction. ​

Answer 1

Correct Question :

The numerator of the fraction is 3 less than the denominator. If 1 is added to both its numerator and denominator it becomes 1/2 . Find the fraction.

Given :

• Numerator of a fraction is 3 less than its Denominator .
• If 1 is added to both its numerator and denominator it becomes 1/2 .

To Find :

• Original Fraction .

Solution :

$\longmapsto\tt{Let\:Denominator\:be=x}$

As Given that Numerator of a fraction is 3 less than its Denominator . So ,

$\longmapsto\tt{Numerator=x-3}$

Now ,

• If 1 is added to both its numerator and denominator it becomes 1/2 .

$\longmapsto\tt{Numerator=x-3+1=x-2}$

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

A.T.Q :

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

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

$\longmapsto\tt{2x-4=1x+1}$

$\longmapsto\tt{2x-1x=1+4}$

$\longmapsto\tt\bf{x=5}$

Value of x is 5 ..

Therefore :

$\longmapsto\tt{Numerator=5-3}$

$\longmapsto\tt\bf{2}$

$\longmapsto\tt\bf{Denominator=5}$

So , The Fraction is 2/5 .

Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

⟼ Let Denominator be= x

As Given that Numerator of a fraction is 3 less than its Denominator . So ,

⟼ Numerator= x−3

Now ,

If 1 is added to both its numerator and denominator it becomes 1/2 .

⟼ Numerator =x−3+1= x−2

⟼ Denominator= x+1

A.T.Q :

⟼ x+1/x−2 = 2/1

⟼ 2(x−2)=1(x+1)

⟼ 2x−4= 1x+1

⟼ 2x−1x= 1+4

⟼x= 5

Value of x is 5 ..

Therefore :

⟼ Numerator =5−3

⟼2

⟼Denominator= 5

So , The Fraction is 2/5 .