Question

the numerator of a 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 then new fraction will be 5/3 fnd 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,
$3(3x + 6) = 5(x + 6)$
$9x + 18 = 5x + 30$
$9x - 5x = 30 - 18$
$4x = 12$
$x = 3$
denominator= x = 3
Given that numerator 2 less than 3 times the denominator
w.k.t. Denominator : 3
3 times 3 is 9
and 9 - 2 =7
Therefore Numerator is 7
And fraction is :-
$\frac{7}{3}$