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 numbers​

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:-

• The rational number

⚘Solution:-

According to the given statement:-

• Let the numerator be x
• Let the denominator be x + 8

$➺\large\bf \frac{x + 17}{x + 8 - 1} = \frac{3}{2}$

$➺\large\bf \frac{x + 17}{x + 7} = \frac{3}{2}$

(Cross multiplying the equations)

➺ 3(x + 1) = 2(x + 17)

➺ 3x + 21 = 2x + 34

➺ 3x - 2x + 21 - 34 = 0

➺ x - 13 = 0

➺ x = 13

So the numerator x = 13

and the denominator x + 8 = 13 + 8 = 21

$\boxed {\sf{ \pink{Hence \: the \: Fraction \: is \: \frac{13}{21}}}}$

Answer 2

• 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 condition,

x+17 3

x+8−1 2

x+17 3

x+7. 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

= x

x+8

= 13

13+8

• Rational number = 13/21

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