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 32 . Find the rational number .​

Answer 1

Answer:

Given that :

1. Denominator of a rational number > Numerator by 8
2. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained = $\frac{3}{2}$

Let the numerator = x

Therefore, according to the question,  

The denominator= x + 8  

[Denominator of a rational number > Numerator by 8]

So, The given rational number = $\frac{x}{x+8}$  ---------------------------[1]

Now, the equation =

= $\frac{x+17}{x+8-1} = \frac{3}{2}$  

=> $\frac{x+17}{x+7} = \frac{3}{2}$

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

=> 3x + 21 = 2x + 34         [Opening the brackets]

=> 3x – 2x + 21 – 34 = 0

=> x – 13 = 0

=> x = 13

Hence, x= 13

Therefore, the rational number = $\frac{x}{x+8}$                 [ By 1 ]

Substituting the value of x, we get:

= $\frac{(13)}{(13) + 8}$

= $\frac{13}{21}$

The given rational number= $\frac{13}{21}$

Answer 2

Answer:

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