Question

The numerator of rational number is 2 less than 3 times of its denominator.if 8 is added to its numerator and 6 is added to its denominator. Than new fraction is 5/3.find that fraction

Answer 1

let the denominator be x
numerator = 3x - 2

fraction is,
$\frac{3x - 2}{x}$
according to the question,

$\frac{3x - 2 + 8}{x + 6} = \frac{5}{3}$

$\frac{3x + 6}{x + 6} = \frac{5}{3}$

therefore,

$3(3x + 6) = 5(x + 6)$

$9x + 18 = 5x + 30$
$9x - 5x = 30 - 18$

$4x = 12$

$x = \frac{12}{4}$

x = 3

numerator = 3x -2 = 7
denominator= x = 3

fraction is

$\frac{7}{3}$