Question

37. The denominator of a rational number is greater than its numerator by 8.
If the numerator is increased by 17 and the denominator is decreased by 1,

the number obtained is 3%2 Find the rational number
​

Answer 1

Answer:

EI2

Step-by-step explanation:

Answer 2

Answer:

$\bigstar{\bold{Rational\:number=\dfrac{13}{21}}}$

Step-by-step explanation:

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

• Denominator is greater than numerator by 8
• If numerator is increased by 17 and denominator is decreased by 1, the number is 3/2

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

• The rational number

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

→ Let the numerator be x

→ Hence by given, denominator would be x + 8

→ Hence the rational number is x/x+8

→ By given,

  $\dfrac{x+17}{x+8-1} =\dfrac{3}{2}$

→ Simplifying,

   $\dfrac{x+17}{x+7}=\dfrac{3}{2}$

→ Cross multiplying we get,

   2 (x + 17) = 3 (x + 7)

   2x + 34 = 3x + 21

   3x - 2x = 34 -21

     x = 13

→ Hence the numerator is 13

→ Denominator = x + 8

  Denominator = 13 + 8

  Denominator = 21

→ Hence the fraction is x/x+8 = 13/21

$\boxed{\bold{Rational\:number=\dfrac{13}{21}}}$

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

→ The rational number is 13/21

→ Increasing the numerator by 17 and decreasing denominator by 1 we get,

  $\dfrac{13+17}{20-1} =\dfrac{30}{20} =\dfrac{3}{2}$

→ Hence verified