Question

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

Answer 1

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Answer

• Let the numerator of the rational number be x
• Denominator = x + 8

☞Rational number =x / x+8

• Given,

☞ x + 17 / x + 8 - 1 = 3 / 2

☞ 2x + 34 = 3x + 21

☞ 34 - 21 = 3x - 2x

☞ 13 = x

☞ x = 13

➜ Therefore,

13 / 13 + 8 = 13 / 21

Answer 2

★ Solution:

Let the numerator be x.

According to the question,

The denominator is greater than the numerator by 8.

So, if the numerator is x; the denominator would be (x + 8)

$\sf{Rational \: number \: \to \: \dfrac{x}{x + 8} }$

Also,

• Numerator is increased by 17
• Denominator is decreased by 1.

→ The number so obtained = 3/2

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

On simplifying,

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

Performing cross multiplication,

$\dashrightarrow \: \: \sf{2(x + 17) = 3(x + 7)}$

$\dashrightarrow \: \: \sf{2x + 34 = 3x + 21 }$

$\dashrightarrow \: \: \sf{34 - 21 = 3x - 2x}$

$\dashrightarrow \: \: \bold{x = 13}$

Now let's find out the rational number.

$\sf{Rational \: number \: \to \: \dfrac{x}{x + 8} }$

Substitute the value of x

$\hookrightarrow \: \: \sf{Rational \: number = \dfrac{13}{13 + 8} }$

$\therefore \: \boxed{ \bf{Rational \: number = \dfrac{13}{21} }}$