Question

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 :-

The numerator of a r ational 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 :-

Rational number

Solution :-

Let the numerator be a

Then denominator = a + 8

Fraction = a/a + 8

When number is multiplied by 3 and 10 is added to denominator

3a/a + 8 + 10 = 21/25

3a/a + 18 = 21/25

25(3a) = 21(a + 18)

75a = 21a + 378

75a - 21a = 378

54a = 378

a = 378/54

a = 7

Then

Fraction = a/a + 8 = 7/15

Answer 2

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 ..