Question

the denominator of sectional number is greater than its numerator by8 . if the numerator is increased by 17and denominotar is decreased by 1 the number obtained is 3/2 . find the rational number.
​

Answer 1

GIVEN:-

• The denominator of sectional number is greater than its numerator by 8

• The numerator is increased by 17and denominotar is decreased by 1 the number obtained is 3/2.

To Find:-

• The Rational Number.

Now,

Let the Numerator be "x"

→ Denominator = x + 8

Now Atq.

→ $\sf{ \dfrac{ x + 17 }{ x + 8 - 1} = \dfrac{3}{2}}$

→ $\sf{ \dfrac{ x + 17 }{ x + 7} = \dfrac{3}{2}}$

→ $\sf{ 2 ( x + 17 ) = 3 ( x + 7 )}$

→ $\sf{ 2x + 34 = 3x + 21 }$

→ $\sf { 2x - 3x = 21 - 34 }$

→ $\sf{ - x = -13}$

→ $\sf{ x = 13 }$.

So, The value of x is 13

→ Numerator = x → 13

→ Denominator = x + 8 → 13 + 8 → 21

Hence, The Rational number is ${\boxed{\underline{\rm{\dfrac{13}{21}}}}}$

VERIFICATION:-

The numerator is increased by 17and denominotar is decreased by 1 the number obtained is 3/2.

→ $\sf{ \dfrac{13}{21}}$

→ $\sf{ \dfrac{ 13 + 17}{ 21 - 1}}$

→ $\sf{ \dfrac{ 30 }{ 20}}$

→ $\sf{ \dfrac{ 3}{ 2} = \dfrac{3}{2}}$.

Hence, Verified

Answer 2

Answer:

Let the Numerator be n and Denominator be (n + 8) of the Fraction respectively.

$\underline{\bigstar\:\textsf{According to the given Question :}}$

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

$:\implies\sf \dfrac{n + 17 }{(n + 8) - 1} = \dfrac{3}{2}\\\\\\:\implies\sf \dfrac{n + 17 }{n + 7} = \dfrac{3}{2}\\\\\\:\implies\sf 2 (n + 17 ) = 3 (n + 7 )\\\\\\:\implies\sf 2n + 34 = 3n + 21\\\\\\:\implies\sf 34-21=3n-2n\\\\\\:\implies\sf n=13$

⠀

$\dag\:\underline{\boxed{\sf Original\:Fraction=\dfrac{n}{n + 8} = \dfrac{13}{(13 + 8)} = \dfrac{13}{21} }}$