Question

5. 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.
(CBSE 2006C]
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Answer 1

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

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

Answer 2

Answer:

Let the required fraction be x/y then,

x + y = 12, ----> (1)

also,

$\frac{x}{y + 3} = \frac{1}{2}$

2x - y = 3 ---> (2)

On adding 1 and 2 we get ;

x = 5

and on putting x = 5 in (1) we get,

5 + y = 12

y = 7

Thus, x = 5 and y = 7

and the required fraction is 5/7.