Question

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

please say answer......​

Answer 1

Correct Question:-

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

To Find:-

• Find the rational number.

Given:-

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

Solution:-

Let the Numerator be be " x "

Denominator be " x + 8 "

According to Question:-

Numerator increased by 17 and the denominator is decreased by 1 , the number obtained is 3/2.

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

$\tt\implies \: 2( x + 17 ) = 3( x + 7 )$

$\tt\implies \: 2x + 34 = 3x + 21$

$\tt\implies \: 3x - 2x = 34 - 21$

$\tt\implies \: x = 13$

Hence,

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

Therefore rational number is 13/21

Answer 2

Correct Question:-

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

To Find:-

Find the rational number.

Given:-

The denominator of a rational number is greater than its numerator by 8.

If the numerator increased by 17 and the denominator is decreased by 1 , the number obtained is 3/2.

Solution:-

Let the Numerator be be " x "

Denominator be " x + 8 "

According to Question:-

Numerator increased by 17 and the denominator is decreased by 1 , the number obtained is 3/2.

${x + 17}{x + 7}$

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

$2x + 34 = 3x + 21$

$3x - 2x = 34 - 21$

$x = 13⟹x=13$

Hence,

Numerator = 13

Denominator is

$x + 8 = 13 + 8 = 21$

Therefore rational number is 13/21