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 1

Answer:

Correct answer is

21/13

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:

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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 xx+8xx+8

According to the given condition,

x+17x+8−1=32x+17x+8−1=32

 

x+17x+7=32x+17x+7=32

 

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

= xx+8xx+8

= 1313+8