Question

[7]. 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.
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Answer 1

Given :

• 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.

To Find :

• Original Rational Number .

Solution :

let,

• the number be X.
• Denominator = x + 8

Now ,

• Numerator = x + 17
• Denominator = x + 8−1 =x+7

Now,

According to Question

$\sf:\implies{\dfrac{x+17}{x+7}=\dfrac{3}{2}}$

$\sf:\implies{2(x+17)=3(x+7)}$

$\sf:\implies{2x+34=3x+21}$

$\sf:\implies{2x-3x=21-34}$

$\sf:\implies{-x=-13}$

$\bf : \implies \red{x = 13}$

Value of x is 13 .

Therefore :

• Numerator = x =13
• Denominator = 13 + 8 = 21

So , The Fraction is 13/21

Answer 2

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