Question

the denominator of a rational number is greater than its numerator by 8. if the numeris increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. find the rational number​

Answer 1

⇝ Correct 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

⇝ Given :-

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.

⇝ To Find :-

The Rational Number.

⇝ Solution :-

Let Numerator and Denominator of Original Rational Number be :

Numerator = x

Accordingly :

Denominator should be = x + 8

So ,

$\text{Original Number = } \frac{\text x}{\text x + 8}$

❒ When Numerator is increased by 17 and the denominator is decreased by 1 :

$\text{Number Becomes : } \frac{\text x + 17}{\text x + 7}$

⏩ According To Question :

$\frac{\text x + 17}{\text x + 7} = \frac{3}{2}$

$:\longmapsto2(\text x + 17) = 3(\text x + 7)$

$:\longmapsto2\text x + 34 = 3\text x + 21$

$:\longmapsto2\text x - 3\text x = 21 - 34$

$:\longmapsto \cancel - \text x = \cancel - 13$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 13} }}}$

So,

$\text{Original Number = } \frac{13}{13+ 8}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{ Original \: Number = \dfrac{13}{21} }}}}}$

Answer 2

Answer:

the denominator of a rational number is greater than its numerator by 8. if the numeris increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. find the rational numb