Question

the denominator of a rational number is greater than its denominator by 8 if thw numinator is increased by 17 and the denominator is decreased by 1 the number obtained is 3/2 find the rational number ​

Answer 1

Answer:

Step-by-step explanation:Suppose numerator of the rational number is p, then denominator is p+8.

Rational number is  

p+8

p

​

.

Numerator is increased by 17, then it becomes p+17.

Denominator is decreased by 1, then it becomes p+8−1=p+7

New rational number is  

p+7

p+17

​

=  

2

3

​

 

⇒2p+34=3p+21

⇒p=13

Thus numerator is 13.

Denominator is p+8=13+8=21

Therefore, the rational number is  

21

13

​

.

Answer 2

Answer:

13/21

Step-by-step explanation:

Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 8.

The rational number will be \(\frac{x}{x+8}\)

According to the given condition,

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

\(\frac{x+17}{x+7} = \frac{3}{2}\)

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

3x + 21 = 2x + 34

3x – 2x + 21 – 34 = 0

x – 13 = 0

x = 13

The rational number will be

= \(\frac{x}{x+8}\)

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

Rational number = 13/21