Question

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Answer 1

Question:

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:

$\bigstar{\bold{The\:number\:is\: \dfrac{13}{21} }}$

Step-by-step explanation:

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

• The denominator is greater than numerator by 8.

• If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2.

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

• The rational number

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

→ Let the numerator be x. Hence by the give data, denominator will be x+8

→ Also by the given data,

  $\dfrac{x+17}{x+8-1} =\dfrac{3}{2}$

 $\dfrac{x+17}{x+7} =\dfrac{3}{2}$

→ Cross multiplying we get,

  2(x + 17) = 3(x + 7)

  2x + 34 = 3x +21

   x = 13

→ The numerator is 13

→ Denominator is x+8 = 13+8 =21

$\boxed{\bold{The\:number\:is\:\dfrac{13}{21} }}$

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

→ The number is 13/21. Adding 17 to numerator and subtracting 1 from denominnator we get 30/20 which is equal to 3/2.

Hence verified.