Question

(4) The numerator of a rational number is 8 less than its denominator.If the numerator is multiplied by 3 and 10 is added to the denominator the new rational number is 21/25. Find the original rational number. ​

Answer 1

Given :

• Numerator of a rational number is 8 less than its denominator.
• If the numerator is multiplied by 3 and 10 is added to the denominator the new rational number is 21/25.

To Find :

• Original Rational Number .

Solution :

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

As Given that Numerator of rational number is 8 less than its Denominator. So ,

$\longmapsto\tt{Numerator=x-8}$

Now ,

• If the numerator is multiplied by 3 and 10 is added to the denominator the new rational number is 21/25.

$\longmapsto\tt{Numerator=3(x-8)=3x-24}$

$\longmapsto\tt{Denominator=x+10}$

A.T.Q :

$\longmapsto\tt{\dfrac{3x-24}{x+10}=\dfrac{21}{25}}$

$\longmapsto\tt{25(3x-24)=21(x+10)}$

$\longmapsto\tt{75x-600=21x+210}$

$\longmapsto\tt{75x-21x=210+600}$

$\longmapsto\tt{54x=810}$

$\longmapsto\tt{x=\cancel\dfrac{810}{54}}$

$\longmapsto\tt\bf{x=15}$

Value of x is 15 ..

Therefore :

$\longmapsto\tt{Numerator=15-8}$

$\longmapsto\tt\bf{7}$

$\longmapsto\tt\bf{Denominator=15}$

So , The Original Rational Number is 7/15 ..