Question

The denominator of a fraction is 5 more than its numerator. if 2 is subtracted from both the numerator
and the denommator, the fraction becomes 4/5.find the fraction.​

Answer 1

Given :

• The denominator of a fraction is 5 more than its numerator.
• If 2 is subtracted from both the numerator and the denominator, the fraction become 4/5.

To Find :

• Original Fraction .

Solution :

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

As Given that denominator of a fraction is 5 more than its Numerator. So ,

$\longmapsto\tt{Denominator=x+5}$

Now ,

• If 2 is subtracted from both the numerator and the denominator, the fraction becomes 4/5.

$\longmapsto\tt{Numerator=x-2}$

$\longmapsto\tt{Denominator=x+5-2=x+3}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-2}{x+3}=\dfrac{4}{5}}$

$\longmapsto\tt{5(x-2)=4(x+3)}$

$\longmapsto\tt{5x-10=4x+12}$

$\longmapsto\tt{5x-4x=12+10}$

$\longmapsto\tt\bf{x=22}$

Value of x is 22 ...

Therefore :

$\longmapsto\tt\bf{Numerator=22}$

$\longmapsto\tt{Denominator=22+5}$

$\longmapsto\tt\bf{27}$

So , The Fraction is 22/27 ...

Answer 2

Question:-

The denominator of a fraction is 5 more than its numerator. if 2 is subtracted from both the numerator and the denommator, the fraction becomes 4/5.find the fraction.

Given:-

• Denominator of fraction is 5 more than the numerator. So, x/x + 5
• Again, if we subtract 2 from the numerator the number becomes 4/5

Solution:-

Let the Numerator be "x"

Denominator be = x + 5

➣ ( x- 2 )/(x + 5 - 2 ) = 4/5 .....( 1 )

➣ ( x - 2 )/( x + 3 ) = 4/5

➣ 5( x - 2 ) = 4( x + 3 )

➣ 5x - 10 = 4x + 12

➣ 5x - 4x = 12 + 10

➣ x = 22

Therefore:-

➣ Numerator = 22

➣ Denominator = 22 + 5 => 27

So,

Fraction is 22/27

Substitute " x " in the equation ( 1 ):-

➣ ( x- 2 )/( x + 5 - 2 ) = 4/5

➣ ( 22 - 2 )/( 22 + 5 - 2 ) = 4/5

➣ 20/25 = 4/5

➣ 4/5 = 4/5