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 number​

Answer 1

Question -

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

Solution -

The number is

$Number = \frac{numerator}{denominator}$

Let the numerator be x

Given,

Denominator is greater than numerator by 8

Denominator =x+8

So,our number becomes

$Number = \frac{x}{x + 8}$

Also given that,

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

So,

$\frac{3}{2} = \frac{x + 17}{(x + 8) - 1}$

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

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

$3x + 21 = 2x + 34$

$3x - 2x = 34 - 21$

$x = 13$

$Number = \frac{x}{x + 8}$

$Number = \frac{13}{13 + 8} = \frac{13}{21}$

$\therefore \: the \: required \: rational \: number \: is \: \frac{13}{21}$

Answer 2

Answer:

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

Solution -

The number is

Number = \frac{numerator}{denominator}Number=

denominator

numerator

Let the numerator be x

Given,

Denominator is greater than numerator by 8

Denominator =x+8

So,our number becomes

Number = \frac{x}{x + 8}Number=

x+8

x

Also given that,

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

So,

\frac{3}{2} = \frac{x + 17}{(x + 8) - 1}

2

3

=

(x+8)−1

x+17

\frac{3}{2} = \frac{x + 17}{x + 7}

2

3

=

x+7

x+17

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

3x + 21 = 2x + 343x+21=2x+34

3x - 2x = 34 - 213x−2x=34−21

x = 13x=13

Number = \frac{x}{x + 8}Number=

x+8

x

Number = \frac{13}{13 + 8} = \frac{13}{21}Number=

13+8

13

=

21

13

\therefore \: the \: required \: rational \: number \: is \: \frac{13}{21}∴therequiredrationalnumberis

21

13