Question

The denominator of a rational number is greater than its numerator by 7. if the numerator is increased by 17 and the denominator is decreased by 6, the new number become 2. find the original number.​

Answer 1

Answer:

15

Step-by-step explanation:

let number =X

then Deni =X+7

(X+17)/(X+7-6)=2

2x-x=17-2

X=15

Answer 2

Answer:

$\bigstar{\bold{The\:number=\dfrac{15}{22} }}$

Step-by-step explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

• Denominator is greater than the numerator by 7
• If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2

$\Large{\underline{\underline{\it{To\:Find:}}}}$

• The original number

$\Large{\underline{\underline{\it{Solution:}}}}$

→ Let the numerator of the rational number be x

→ Hence by given,

  Denominator = x + 7

→ Therefore,

  $\sf{The\:rational\:number=\dfrac{x}{x+7}}$

→ Also by given, if the numerator is increased by 7 and denominator decreased by 17, the number becomes 2.

→ Hence,

  $\sf{\dfrac{x+17}{x+7-6} =\dfrac{2}{1} }$

  $\sf{\dfrac{x+17}{x+1} =\dfrac{2}{1}}$

→ Cross multiplying,

  1 ( x + 17 ) = 2 (x + 1)

→ Simplifying,

  x + 17 = 2x + 2

  2x - x = 17 - 2

  x = 15

→ Hence the numerator of the fraction is 15

→ The denominator of the fraction is given by

   Denominator = x + 7

   Denominator = 15 + 7

   Denominator = 22

→ Hence the denominator of the fraction is 22

→ Therefore,

   $\boxed{\bold{The\:number=\dfrac{15}{22} }}$

$\Large{\underline{\underline{\it{Verification:}}}}$

→ Denominator = Numerator + 7

  22 = 15 + 7

  22 = 22

→ If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2

 $\sf{\dfrac{15+17}{22-6} =\dfrac{2}{1} }$

  $\sf{\dfrac{32}{16}=\dfrac{2}{1} }$

  $\sf{\dfrac{2}{1}=\dfrac{2}{1} }$

→ Hence verified.