Question

in a rational number, denominator is 5 more then the numberator. if 2 is added to the numberator and 2 is substracted from the denominayor the rational number becomes 5/6.find the fraction.
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Answer 1

Given :

• In a rational number, denominator is 5 more then the numerator. if 2 is added to the numerator and 2 is subtracted from the denominator the rational number becomes 5/6.

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To Find :

• Find the original fraction.

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Solution :

~ According to the Question :

✏ The denominator is 5 more then the numerator. Hence,

$\qquad{\large{\bigstar{\underline{\overline{\boxed{\sf{ \dfrac{Numerator}{Denominator} = \dfrac{x}{x + 5}}}}}}}{\bigstar}}$

✏ If 2 is added to the numerator and 2 is subtracted from the denominator the fraction becomes 5/6. Hence,

$\qquad{\large{\bigstar{\underline{\overline{\boxed{\sf{ \dfrac{x + 2}{x + 5 - 2} = \dfrac{5}{6}}}}}}}{\bigstar}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

~ Now, Let's Cross - Multiply :

➻ Cross multiplying the values :

${:\longmapsto{\qquad{\sf{ 6(x + 2) = 5(x + 5 - 2)}}}}$

➻ Subtracting the RHS side :

${:\longmapsto{\qquad{\sf{ 6(x + 2) = 5(x + 3)}}}}$

➻ Multiplying the LHS and RHS side :

${:\longmapsto{\qquad{\sf{ 6x + 12 = 5x + 15}}}}$

➻ Transporting 5x to LHS side and 12 to RHS side :

${:\longmapsto{\qquad{\sf{ 6x - 5x = 15 - 12}}}}$

➻ Value of x :

$\large{\qquad{\red{:\longmapsto}}{\underline{\boxed{\red{\sf{x = 3 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

~ Numerator and Denominator :

$➬{\orange{\sf{Numerator = x = 3 }}}$

$➬{\orange{\sf{Denominator = x + 5 = 3 + 5 = 8}}}$

~ Original Fraction :

$\large{\red{\underline{\blue{\underline{\pink{\pmb{\frak{ Original \: Fraction \: = \dfrac{3}{8}}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

~ Therefore :

‎‎‎‎‎‎‎‎‎‏‏‎ ‎‏‏‎ ‎‏‏‎❝ Original fraction is 3/8 .❞

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