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

Answer:

13/21

Step-by-step explanation:

let the numerator be x then

(x+17)/(x+8-1) =3/2

by cross multiplying

2x+34 = 3x+21

taking all the variables to one side we get

34-21 = 3x-2x

13=x .

the rational number is 13/(13+8)

13/21

Answer 2

AnswEr

The required rational number is 13/21

GivEn

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

• When 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

Let us consider the numerator and denominator be x and y respectively

Therefore , the rational number will be :

$\sf \longrightarrow \dfrac{x}{y}$

According to question

$\sf \implies y = x + 8 \dashrightarrow(1)$

Again by question

$\sf\implies \dfrac{x+17}{y-1} = \dfrac{3}{2} \\\\ \sf\implies 2(x + 17)= 3(y - 1) \\\\ \sf\implies 2(x + 17) = 3(x + 8 - 1) \: \: \: \{ \because y = x + 8 \: from \: (1)\} \\\\ \sf\implies 2(x + 17) = 3(x + 7) \\\\ \sf\implies 2x + 34 = 3x + 21 \\\\ \sf\implies 2x-3x = 21-34 \\\\ \sf\implies -x = -13 \\\\ \sf\implies x = 13$

Putting the value of x in (1)

$\sf\implies y = 13 + 8 \\\\ \sf\implies y = 21$

Hence the required rational number is

$\bf \hookrightarrow \dfrac{13}{21}$