Question

X:
The denominator of a rational number is
greater than its numerator by 8 If
numerator is increased by, 17 and the 7t8
denominator is decreased by 1, the
number obtained is 3\2 . Find the rational
number.​

Answer 1

Answer:

13/21

Step-by-step explanation:

let the numerator be x

denominator= x+8

increased numerator= x+17

decreased denominator= x+8-1= x+7

ATQ, number obtained is 3/2

therefore,

(x+17)/(x+7)=3/2

or, 2(x+17)=3(x+7)

or, 2x+34=3x+21

or, 34-21=3x-2x

or, x=13

therefore numerator= 13 and denominator = 13+8= 21

hence the rational number is 13/21

Answer 2

➝ Let the numerator be x.

ATQ:

The denominator of a rational number is 8 more than its numerator.

➝ The denominator becomes x + 8.

Therefore, the rational number is x/(x + 8)

Now, when the denominator is decreased by 1, and the numerator is increased by 17, the number obtained is 3/2.

$\Longrightarrow \rm \dfrac{x + 17}{x + 8 - 1} = \dfrac{3}{2}$

$\Longrightarrow \rm \dfrac{x + 17}{x + 7} = \dfrac{3}{2}$

$\Longrightarrow \rm 2\big(x + 17\big) = 3\big(x + 7\big)$

$\Longrightarrow \rm 2x + 34 = 3x + 21$

$\Longrightarrow \rm 2x - 3x = 21 - 34$

$\Longrightarrow \rm -x = -13$

$\Longrightarrow \rm x = 13$

Numerator ➝ x ➝ 13

Denominator ➝ x + 8 ➝ 13 + 8 ➝ 21

We know that:

$\Longrightarrow \rm Rational \ number = \dfrac{x}{x + 8}$

$\Longrightarrow \rm Rational \ number = \dfrac{13}{21}$

Therefore, your answer will be 13/21.