Question

The denominator of rational no. Is greater than its numerator by 6.if numerator is increased by 5and denominator by 3 , the no. Obtained is 5/4 . Find rational number.

Answer 1

Hey !!

Let numerator of rational number be X.

So , Denominator of rational = ( X + 6 ).

Rational Number = Numerator / Denominator = X / X + 6.

• Numerator is increased by 5 , Then New Numerator = ( X + 5 ).

• Denominator is increased by 3 , then new Denominator = ( X + 6 - 3 ) = ( X + 3 ).

New Rational Number = New numerator / New Denominator = ( X + 5 ) / ( X + 3 ).

According to the question,

X + 5 / X + 3 = 5/4

4 ( X + 5 ) = 5 ( X + 3 )

4X + 20 = 5X + 15

5X - 4X = 20 - 15


X = 5

Numerator = X = 5

And,

Denominator = ( X + 6 ) = 5 + 6 = 11

Therefore,

Rational Number = Numerator / Denominator = 5/11

Answer 2

Let the numerator of the rational number be x .

Then , the denominator of the rational number

=> x + 6

It is given that the numerator is increased by 5 and the denominator is decreased by 3 .

The numerator of the new numerator = x + 5

Denominator of the new rational number

= ( x + 6 ) - 3

= x + 3

New rational number = x + 5 / x + 3

But the new rational number is given as 5 / 4

x + 5 / x + 3 = 5 / 4

By cross multipication , We get

4 ( x + 5 ) = 5 ( x + 3 )

4x + 20 = 5x + 15

4x - 5x = 15 - 20

- x = - 5

x = 5

Numerator of the rational number = 5

Denominator of the rational number = 5 + 6 , i.e. 11

Rational number = 5 / 11

VERIFICATION :-

Original Numerator + 5 / Original Denominator - 3 = 5 + 5 / 11 - 3

= 10 / 8

= 5 / 4

which is the same as given in the problem .

Hence , the solution is verified .