Question

the numerator of a fraction is 4 less that it's denominator. if 1 is added to both its numerator and denominator, it becomes ⁴/¹². Fund the fraction​

Answer 1

Corrected Question : –

• The numerator of a fraction is 4 less than it's denominator. If 1 is added to both it's numerator and Denominator. Then, it becomes 4/12. Find the fraction.

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❍ Let the Denominator of the fraction be x respectively.

Then, it's Numerator = (x – 4).

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$\underline{\bigstar\:\boldsymbol{According\;to \;the \;given\; Question \;:}}$

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• If 1 is added to both it's numerator and Denominator. Then, it becomes 4/12.

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Therefore,

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$:\implies\sf \dfrac{(x - 4) + 1}{x + 1} = \dfrac{4}{12}\\\\\\:\implies\sf \dfrac{x - 3}{x + 1} = \dfrac{4}{12} \\\\\\:\implies\sf 12(x - 3) = 4(x + 1)\\\\\\:\implies\sf 12x - 36 = 4x + 4\\\\\\:\implies\sf 12x - 4x = 4 + 36\\\\\\:\implies\sf 8x = 40\\\\\\:\implies\sf x = \cancel\dfrac{40}{8}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\;\bigstar$

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Hence,

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• Numerator of fraction, (x – 4) = (5 – 4) = 1
• Denominator of fraction, x = 5

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$\therefore{\underline{\sf{Hence, \;the\; required\; fraction\;is\;\bf{\dfrac{1}{5}}.}}}$

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V E R I F I C A T I O N :

• If 1 is added to both it's numerator and Denominator. Then, it becomes 4/12. Let's verify :

$\dashrightarrow\sf \dfrac{1}{5} = \dfrac{4}{12} \\\\\\\dashrightarrow\sf \dfrac{1 + 1}{5 + 1} = \cancel\dfrac{4}{12} \\\\\\\dashrightarrow\sf \cancel\dfrac{2}{6} = \cancel\dfrac{2}{6} \\\\\\\dashrightarrow\underline{\boxed{\frak{ \dfrac{1}{3} = \dfrac{1}{3}}}}$

$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}$

Answer 2

Let the denominator be = d

∴ Numerator = (d - 4)

If 1 is added to both numerator and denominator, then the fraction becomes = 4/12 or ⅓

So, as per condition:

[(d - 4) + 1]/[(d) + 1] = ⅓

⇒ (d - 3)/(d + 1) = ⅓

By cross multiplication,

⇒ 3(d - 3) = d + 1

⇒ 3d - 9 = d + 1

⇒ 3d - d = + 1 + 9

⇒ 2d = 10

⇒ d = 5.

So, fraction: (5 - 4)/5 = ⅕.