Question

The denominator of a fraction is 3 more than the numerator.if 5 is added to both numerator and denominator the fraction becomes4/5.find the fraction

Answer 1

check attachment for the answer

Answer 2

Given:

• The Denominator of a fraction is two more than the Numerator. If 1 is added to Both the Numerator and Denominator then fraction reduces to ⅘.

To find:

• The Original fraction

⠀

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Solution:

• So, Let's Consider that the Numerator of the fraction be x. Then, the Denominator of the fraction be (x + 2) respectively.⠀⠀

• Now, we'll add 1 to both the Numerator and Denominator of the fraction, we Get —

⠀

$\begin{gathered}:\implies\sf \Bigg\{\dfrac{x + 1}{x + 2 + 1}\Bigg\} = \Bigg\{\dfrac{4}{5}\Bigg\} \\\\:\implies\sf \Bigg\{\dfrac{x + 1}{x + 3}\Bigg\} = \Bigg\{\dfrac{4}{5}\Bigg\}\\\\:\implies\sf 5\Big\{x + 1\Big\} = 4\Big\{x + 3\Big\}\\\\:\implies\sf 5x + 5 = 4x + 12\\\\:\implies\sf 5x - 4x = 12 - 5\\\\:\implies\underline{\boxed{\frak{x = 7}}}\; \pink\bigstar\end{gathered}$

Therefore,

• Numerator of fraction, x = 7
• Denominator of fraction, (x + 2) = (7 + 2) = 9⠀

$\boxed{ \sf{Hence, \: the \: required \: fraction \: is \: \bold{\dfrac{7}{9}}.}}$

Thank you!

@itzshivani