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
3
obtained is
Find the rational number.
2​

Answer 1

Answer:

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Step-by-step explanation:

Let us take the nuber as x,

Denominator greater than the numerator by = 8 = x + 8

denominator is decreased by 1 = x + 8 - 1 = x + 7

Numerator is increased by 17 = x + 17

numerator  = x + 17

denominator = x + 7

Lets assume ,

x + 17/x+7 = 3 / 2

2 (x + 17) = 3 (x +7)

2x + 34 = 3x + 21

2x - 3x = 21 - 34

-x = -13

- and - = +

so ,

x = 13

numarator = x = 13

denominator = x + 8 = 21

rational no = 13/21

Hope This Will Help You........

Answer 2

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.

AnswEr :

⠀⠀⠀☯ Denominator of the fraction is greater than it's numerator by 8. Let's assume that number be 'x'.

$:\implies\sf Denominator \: will \: be \: (x + 8).$

$:\implies\sf Fraction = \dfrac{Numerator}{Denominator} = \dfrac{x}{x + 8}$

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Now,

If the Numerator is increased by 17 & the denominator is decreased by 1, Number obtained is 3/2.

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

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${\dag}\:\underline{\frak{Finding\: original \: fraction\: :}}$

$:\implies\sf \dfrac{x}{x + 8} \\\\\\:\implies\sf\dfrac{13}{13 + 8} \\\\\\:\implies\sf\dfrac{13}{21}$

$\therefore\:\underline{\textsf{Required \: number\: is \: \textbf{ {} {\text13}\!/{}_{\text{21}} }}}.$