Question

the denominator of a rational number is greater than it's 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

let numerator = x
  denominator =x+8
if
  numerator is increased by 17 = x+17
denominator is decreased by 1 = x+8-1 = x+7
a.t.q.
         x+17     3
                  ×
         x+7      2
         2(x+17) = 3(x+7)
         2x + 34 = 3x + 21
         34 -21 = 3x - 2x
           13 = x
numerator = x =13
denominator = x+8 = 13 + 8 = 21

Answer 2

Answer :

The required rational number is 13 / 21.

Step-by-step explanation :

Let the numerator be x.

And , denominator = x + 8

Fraction = x / x + 8

According to the question ;

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

⇒ x + 17 / x + 7 = 3 / 2

⇒ 3 ( x + 7 ) = 2 ( x + 17 )

⇒ 3x + 21 = 2x + 34

⇒ 3x - 2x = 34 - 21

⇒ x = 13

Hence,

Required fraction = x / x + 8

                         .    ⇒ 13 / 13 + 8

                         .    ⇒ 13 / 21

Hence, the required fraction is 13 / 21