Question

The denominator of a
rational number its
greater
than the numerator by 8. If the numerator is
increased by 17
and denominator is decreased
by I, the number obtained
is 1/4. Find the
rational
number. plz answer​

Answer 1

Correct Question:-

The denominator of a rational number is greater than its numerator by 8. If numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

Answer:-

Let the number be x/y.

Given:

Denominator is greater than the numerator by 8.

⟶ Denominator = Numerator + 8

⟶ y = x + 8 -- equation (1)

And,

The number becomes 1/4 if 17 is added to numerator and 1 is subtracted from denominator.

$\implies \sf \: \frac{x + 17}{y - 1} = \frac{3}{2}$

Substitute the value of y from equation (1).

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

Substitute the value of x in equation (1).

⟶ y = 13 + 8

⟶ y = 21

Therefore, the required fraction x/y is 13/21.

Answer 2

Answer:

Let the Numerator be a and Denominator be (a + 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

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

⠀

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