Question

7. The denominator of a rational number is greater than its numerator by 8. If the
numerator is increased by 17 and the denominator is decreased by 1, the number
obtained is
3
2 . Find the rational number.

Answer 1

Answer:

The required rational number is $\bf \dfrac{13}{21}$

Step-by-step explanation:

Given :

• The denominator of a rational number is greater than its numerator by 8.
• If the  numerator is increased by 17.
• The denominator is decreased by 1.

To Find :

The rational number.

Solution :

Let the number be - x

So,

Denominator = x + 8

Fraction = x / x + 8

According to the question :

⇒ x + 17 / x + 8 - 1 = 3 / 2

⇒ x + 17 / x + 7 = 3 / 2

⇒ 3 ( x + 7 ) = 2 ( x + 17 )

⇒ 3x + 21 = 2x + 34

⇒ 3x - 2x = 34 - 21

⇒ x = 13

Hence,

The Required fraction :

⇒ x / x + 8

⇒ 13 / 13 + 8

⇒ 13 / 21

Hence,

The required fraction is 13 / 21.

Answer 2

$\huge\mathfrak\blue{Answer:-}$

Given:

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3.

To Find:

The rational number.

Solution:

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  

Hence, the rational number is 13/21.