Question

the denominator of rational number is greater than its numerator by 8 if the numbers is increased by 17 and denominator is increased by once the numerator is obtained is 3 by 2 find the rational number​

Answer 1

${\huge{\underline{\underline{\sf{\blue{Solution :-}}}}}}$

The numerator of the rational number = x.

Then denominator of the rational number = x + 8 .

$Therefore , the rational number = \frac{x}{x + 8}$

${\huge{\underline{\underline{\sf{\blue{ATQ:-}}}}}}$

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

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

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

( By cross multiplication )

$= > \: 2x + 34 = 3x + 21$

$= > \: 34 - 21 = 3x - 2x$

$= > \: 13 = x$

$= > \: x = 13$

Therefore , the numerator = x = 13 , the denominator = x + 8 = 13 + 8 = 21 and the rational number =$\frac{13}{21}$