Question

The denominator of a rational number is greater than its numerator by 8 .jf the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2 . Find the rational number
Chapter: linear equations in one variable​

Answer 1

Answer:

13/21

Step-by-step explanation:

Let the numerator of the rational number be X

Then denominator = X + 8

Therefore, the rational number = X/X + 8

Given,

$\frac{x + 17}{x + 8 - 1} = \frac{3}{2}$

or, 2x + 34 = 3x + 21

or, x = 13

Therefore, the number is

$\frac{13}{13 + 8} = \frac{13}{21}$

Answer 2

Answer:

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

Step-by-step explanation:

Solution :

Let,

• Numerator = x
• Denominator = x + 8

If the numerator is increased by 17 :

• Numerator = x + 17

The denominator is decreased by 1 :

• Denominator = x + 8 - 1 = x + 7

The number obtained is 3/2

So,

★ According to the Question :

⇒ $\dfrac{x \: + \: 17}{x \: + \: 7} \: = \: \dfrac{3}{2}$

⇒ 2 (x + 17) = 3 (x + 7)

⇒ 2x + 34 = 3x + 21

⇒ 34 - 21 = 3x - 2x

⇒ 13 = x

Numerator = 13

• Denominator = x + 8

⇒ x + 8

⇒ 13 + 8

⇒ 21

Denominator = 21

The rational number = $\dfrac{13}{21}$

Therefore, the rational number = $\dfrac{13}{21}$