Question

The denominatior 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 3/2 Find the rational number​

Answer 1

Answer:

Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 8.

The rational number will be x/x + 8.

According to the given cndition,

x + 17/x + 8 – 1 = 3/2

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

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

=2x + 34 = 3x + 21

=34 − 21 = 3x − 2x

=x=13

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number = 13/21

hope it helped you

Answer 2

Question

The denominatior 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 3/2 Find the rational number.

Anwer

$\rm \: let \: the \: numerator \: be \: x$

$\rm \: and\: the \: deniminator \: be \: x + 8$

$\rm \therefore \: the \: rational \: no. = \frac{x}{x + 8}$

$\bf \: according \: to\: the \: question$

$\rm \leadsto \frac{x + 17}{x + 8 - 1} = \frac{3}{2}$

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

$\rm \leadsto {2 (x + 17)} = {3 ( x + 7)}$

$\rm \leadsto {2 x + 34} = {3 x + 21}$

$\rm \leadsto {2 x - 3 x = { + 21} - 34}$

$\rm \leadsto - x = - 13$

$\rm \leadsto x = 13$

$\rm \leadsto \cancel - x = \cancel - 13$

$\tt \therefore \: numerator = x = 13$

$\tt denominator = x+ 8 = 21$

$\boxed {\tt \: the \: rational \: no. = \frac{13}{21}}$