Question

the denominator of a rational number is greater than its numerator by 8 if the numerator is increased by 17 and the denominatorthe 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 by 2 find the rational number​

Answer 1

Answer:

13

Step-by-step explanation:

let the numerator be x

x/x+8

as per the question :

x+17/x+8-1 = x+17/x+7

x+17/x+7 = 3/2

do cross multiplication

2x +34 = 3x + 21

=34-21 = 3x - 2x

therefore , x=13

Answer 2

Answer:

AnswEr:

Let us Consider that the Number be x.

According to Question,

Denominator is Greater than the Numerator by 8.

So, Denominator = x + 8.

Number = $\sf\dfrac{x}{x+8}$

If the Numerator is increased by 17 & the denominator is decreased by 1, Number obtained is $\sf\dfrac{3}{2}$ [Given]

Therefore,

$\implies\sf\: \dfrac{x + 17}{[x +8] -1} = \dfrac{3}{2}$

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

$\:\:\:\:\:\:\;\:\:\:\:\:\:\;\dag\:\:\footnotesize\bold{\underline{\underline{\sf{\red{Cross\: Multiplying}}}}}$

$\implies\sf\: 3(x + 7) = 2(x +17)$

$\implies\sf\: 3x + 21 = 2x + 34$

$\implies\sf\: 3x = 2x + 34 - 21$

$\implies\sf\: 3x = 2x + 13$

$\implies\sf\: 3x - 2x = 13$

$\implies\large\boxed{\sf{\purple{ x\:=\:13}}}$

Now, Finding Number

$\implies\sf\: \dfrac{x}{x + 8}$

$\implies\sf\: \dfrac{13}{13 + 8}$

$\implies\sf\: \dfrac{13}{21}$

Hence, Required Number is $\sf\dfrac{13}{21}.$

$\rule{250}2$