Question

The sum of the numerator and denominator of a fraction is 12.If the denominator is increased by 3,the fraction becomes 1/2.find the fraction

Answer 1

Answer:

hope it helped you and thanks for asking

Answer 2

Step-by-step explanation:

AnswEr :

⠀⠀⠀Let us consider that Numerator be x & Denominator be y. So, Our fraction is - $\sf\dfrac{Numerator}{Denominator} = \dfrac{x}{y}$

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

⠀⠀⠀Sum of numerator & denominator is 12 & when denominator increased by 3 fraction becomes $\sf\dfrac{1}{2}$

$:\implies\sf x + y = 12 \\\\\\:\implies\sf \dfrac{x}{y + 3} = \dfrac{1}{2} \\\\\\:\implies\sf x = \dfrac{1}{2} (y + 3) \\\\\\:\implies\sf \dfrac{1}{2} (y + 3) + y = 12 \\\\\\:\implies\sf y + 3 + 2y = 24 \\\\\\:\implies\sf 3y = 24 - 3 \\\\\\:\implies\sf 3y = 21 \\\\\\:\implies\sf y = \dfrac{21}{3} \\\\\\:\implies\sf\underline{\boxed{\sf y = 7}}$

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$:\implies\sf x + y = 12 \\\\\\ :\implies\sf x + 7 = 12 \\\\\\:\implies\sf x = 12 - 7 \\\\\\ :\implies\sf\underline{\boxed{\sf x = 5}}$

$\therefore\:\underline{\textsf{Required \: fraction \: is \: \textbf{ {} {\text5}\!/{}_{\text{7}} }}}.$