Math, asked by aditisinha87, 9 months ago

The numerator and denominator of a rational number are in the ratio 3:4. If the
denominator is increased by 3, the ratio becomes 3:5. Find the rational number.

Answers

Answered by Anonymous
6

Let the numerator be 3x

Let the denominator be 4x

Increased denominator = 4x+3

A.T.P

3x/4x+3=3/5

Cross multiplying

15x=12x+9

15x-12x=9

3x=9

x=3

3x=3*3=9

4x=4*3=12

Therefore the rational number

=9/12

=3/4(Answer)

Hope it helped you.....

Answered by SugaryCherrie
4

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 ...

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