Question

The denominator of a rational number is greater than its numerator by 8.If the numerator is incresed by 17 and the denominator is increased by 1 the number obtained 3/2.Find the number
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Answer 1

Answer:

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 x/x + 8.

According to the given cndition,

x + 17/x + 8 – 1 = 3/2

=x + 17/x + 7 = 3/2

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

=2x + 34 = 3x + 21

=34 − 21 = 3x − 2x

=x=13

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number = 13/21

Answer 2

Answer:

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

.