Question

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 obtain is 3/2 find the rational number

Answer 1

Answer:

31/39

Step-by-step explanation:

Let the numerator be X.

Given,

X/X+8

X+17/X+1=3/2

Upon cross multiplication,

2X+34=3X+3

31=X,the numerator.

Therefore,the fraction is 31/39.

Answer 2

Step-by-step explanation:

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 $\sf\dfrac{13}{21}.$

$\rule{250}2$