Question

11 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 is3/2. Find the rational number​

Answer 1

Let, the numerator be x

Then, the denominator would be x+8

It is also mentioned that adding 17 and decreasing 1 from the numerator and denominator respectively we get 3/2

So, we got an equation to compute -

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

∵ x = 13,

• Numerator = x = 13
• Denominator = x+8 = 13+8 = 21

So, the required rational number would be $\frac{13}{21}$

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Answer 2

Answer:

Let, the numerator be x

Then, the denominator would be x+8

It is also mentioned that adding 17 and decreasing 1 from the numerator and denominator respectively we get 3/2

So, we got an equation to compute -

\begin{gathered}\frac{x+17}{(x+8)-1} =\frac{3}{2} \\\\\frac{x+17}{x+7} =\frac{3}{2}\\\\2(x+17)=3(x+7)\\\\2x+34=3x+21\\\\3x-2x=34-21\\\\x=13\end{gathered}

(x+8)−1

x+17

=

2

3

x+7

x+17

=

2

3

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

2x+34=3x+21

3x−2x=34−21

x=13

∵ x = 13,

Numerator = x = 13

Denominator = x+8 = 13+8 = 21

So, the required rational number would be \frac{13}{21}

21

13

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