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. Find the rational 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 [latex]\frac{x}{x+8}[/latex]

According to the given condition,

[latex]\frac{x+17}{x+8-1} = \frac{3}{2}[/latex]

[latex]\frac{x+17}{x+7} = \frac{3}{2}[/latex]

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

= [latex]\frac{x}{x+8}[/latex]

= [latex]\frac{13}{13+8}[/latex]

Rational number = 13/21

Answer 2

Answer:

Correct option is

A

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