Question

the denominator of a rational numbers is greater than its numerator by 7. If the numerator is increased by 4 and denominator is decreased by 8 the new rational numbers is 8/3​

Answer 1

Answer:

let numerator be x

∴the denominator will be x+8

⇒x+17/x+8-1=3/2

⇒x+17/x+7=3/2

⇒2(x+17)=3(x+7)

⇒2x+34=3x+21

⇒34-21=3x-2x

⇒13=x

∴x/x+8

=13/21 (Ans )

Answer 2

Given :

• Denominator of a Rational Number is greater than its numerator by 7 .
• If the numerator is increased by 4 and denominator is decreased by 8 the new rational numbers is 8/3 .

To Find :

• Original Rational Number .

Solution :

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

As Given that the Denominator of a rational numbers is greater than its Numerator by 7. So ,

$\longmapsto\tt{Denominator=x+7}$

Now ,

• If the numerator is increased by 4 and denominator is decreased by 8 the new rational numbers is 8/3 .

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

$\longmapsto\tt{Denominator=x+7-8=x-1}$

A.T.Q :

$\longmapsto\tt{\dfrac{x+4}{x-1}=\dfrac{8}{3}}$

$\longmapsto\tt{8(x-1)=3(x+4)}$

$\longmapsto\tt{8x-8=3x+12}$

$\longmapsto\tt{8x-3x=12+8}$

$\longmapsto\tt{5x=20}$

$\longmapsto\tt{x=\cancel\dfrac{20}{5}}$

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

Value of x is 4 ....

Therefore :

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

$\longmapsto\tt{Denominator=4+7}$

$\longmapsto\tt\bf{11}$

So , The Rational Number is 4/11 ...