Question

The denominator of a fraction is 1 less than 3 times its numerator adding 3 to the numerator and denominator gives 1/2 . Find the fraction

Answer 1

AnswEr :

Let us consider that Numerator be 'x'.

And, Denominator be '3x - 1'. [Denominator is 1 less than 3 times its denominator.]

$:\implies\tt Fraction = \dfrac{Numerator}{Denominator} = \dfrac{x}{3x - 1}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question :}}$⠀

$:\implies\dfrac{x + 3}{3x - 1 + 3} = \dfrac{1}{2}\\\\\\:\implies\tt \dfrac{x + 3}{3x + 2}= \dfrac{1}{2} \\\\\\:\implies\tt 2\Big(x + 3 \Big) = 1 \Big( 3x + 2 \Big) \\\\\\:\implies\tt 2x + 6 = 3x + 2 \\\\\\:\implies\tt 2x + 6 - 3x -2 = 0 \\\\\\:\implies\tt x - 4 = 0 \\\\\\:\implies\tt x = 4\\\\\\:\implies\tt Now, \: fraction = \dfrac{x}{3x -1} = \dfrac{4}{3(4) - 1} \dfrac{4}{12 - 1} \\\\\\:\implies\tt \dfrac{4}{11}$

$\therefore\:\underline{\textsf{Required \: fraction \: is \: \textbf{ {} {\text4}\!/{}_{\text{11}} }}}.$

Answer 2

EXPLANATION.

Let the numerator of a fraction = x

Let the denominator of fraction = 3x - 1

To find the fraction.

According to the question,

adding 3 to the numerator and

denominator gives = 1/2

=> x + 3 / 3x - 1 + 3 = 1/2

=> x + 3 / 3x + 2 = 1/2

=> 2 ( x + 3 ) = 3x + 2

=> 2x + 6 = 3x + 2

=> 4 = x

Therefore,

Numerator = 4

Denominator = 3(4) - 1 = 11

Fraction = 4/11