Question

The ratio of the numerator and the denominator of a rational number is 3:4. If 4 is added to the numerator and 6 is subtracted from the denominator, then the rational number becomes 8/5. Then original rational number is _____.

Answer 1

Given :

• The ratio of Numerator and Denominator of a rational number is 3:4 .
• If 4 is added to the numerator and 6 is subtracted from the denominator, then the rational number becomes 8/5.

To Find :

• The Original Fraction .

Solution :

$\longmapsto\tt{Let\:Numerator\:be=3x}$

$\longmapsto\tt{Let\:Denominator\:be=4x}$

Now ,

• If 4 is added to the numerator and 6 is subtracted from the denominator, then the rational number becomes 8/5.

$\longmapsto\tt{Numerator=3x+4}$

$\longmapsto\tt{Denominator=4x-6}$

A.T.Q :

$\longmapsto\tt{\dfrac{3x+4}{4x-6}=\dfrac{8}{5}}$

$\longmapsto\tt{5(3x+4)=8(4x-6)}$

$\longmapsto\tt{15x+20=32x-48}$

$\longmapsto\tt{15x-32x=-48-20}$

$\longmapsto\tt{-17x=-68}$

$\longmapsto\tt{x=\cancel\dfrac{-68}{-17}}$

$\longmapsto\tt\bf{x=4}$

Value of x is 4...

Therefore :

$\longmapsto\tt{Numerator=3(4)}$

$\longmapsto\tt\bf{12}$

$\longmapsto\tt{Denominator=4(4)}$

$\longmapsto\tt\bf{16}$

So , The Fraction is 12/16 ...

Answer 2

Given :

The ratio of Numerator and Denominator of a rational number is 3:4 .

If 4 is added to the numerator and 6 is subtracted from the denominator, then the rational number becomes 8/5.

To Find :

The Original Fraction .

Solution :

$\longmapsto\tt{Let\:Numerator\:be=3x}$

$\longmapsto\tt{Let\:Denominator\:be=4x}$

Now ,

If 4 is added to the numerator and 6 is subtracted from the denominator, then the rational number becomes 8/5.

$\longmapsto\tt{Numerator=3x+4}$

$\longmapsto\tt{Denominator=4x-6}$

A.T.Q :

$\longmapsto\tt{\dfrac{3x+4}{4x-6}=\dfrac{8}{5}}$

$\longmapsto\tt{5(3x+4)=8(4x-6)}$

$\longmapsto\tt{15x+20=32x-48}$

$\longmapsto\tt{15x-32x=-48-20}$

$\longmapsto\tt{-17x=-68}$

$\longmapsto\tt{x=\cancel\dfrac{-68}{-17}}$

$\longmapsto\tt\bf{x=4}$

Value of x is 4...

Therefore :

$\longmapsto\tt{Numerator=3(4)}$

$\longmapsto\tt\bf{12}$

$\longmapsto\tt{Denominator=4(4)}$

$\longmapsto\tt\bf{16}$

So , The Fraction is 12/16 ...