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 numerator obtained is 3/2.Find the rational number.​

Answer 1

$\huge\tt{\underline{\underline{\underline\blue{Answer}:-}°}}$

Let the numerator be $x$

then,

the denominator = $x+8$

•Required rational number =$\frac{Numerator \: + \: 17 }{Denominator \: - \: 1 }$

⠀⠀⠀⠀ ⠀⠀⠀⠀⠀:•⟹ $\frac{x + 17}{(x + 8) - 1}$

⠀⠀⠀⠀ ⠀⠀⠀⠀⠀:•⟹ $= \frac{x + 17}{x + 7}$

It is given that new rational number = $\frac{3}{2}$

.°. $\frac{x \: + \: 17}{x \: + \: 7} = \frac{3}{2}$

:•⟹ $2(x + 17) = 3(x + 7)$

:•⟹ $2x + 34 = 3x + 21$

:•⟹ $2x - 3x = 21 - 34$

:•⟹ $- x = - 13$

:•⟹ $x = 13$

•Reqd. rational number$=\frac{x}{x + 8} = \frac{13}{13 + 8} =\frac{13}{21}$

Answer 2

Answer:

$⟹ \frac{13}{21}$

Step-by-step explanation:

Let the numerator be X

Then,

The denominator ⟹ X + 8

Require rational number

$\: \: \: \: \: \: \: \: \: \: \: ⟹ \frac{numerator \: + 17}{denomintor \: - 1}$

$⟹ \frac{x + 17}{(x + 8) - 1}$

$⟹ \frac{x + 17}{x + 17}$

It is given that new rational number = 3/2

$∴ \frac{x + 17}{x + 7} = \frac{3}{2}$

$➸2(x + 17) = 3(x + 7)$

$➸2x + 34 = 3x + 21$

$➸2x - 3x = 21 - 34$

$➸ - x = - 13$

$➸x = 13$

Required rational number

$➸ \frac{x}{x + 8}$

$➸ \frac{13}{13 + 8}$

$➸ \frac{13}{21}$