Question

The denominator of a rational no is greater than its numerator by 8.if numerator is increased by 17 and denominator is decreased by 1 the no equals to 3/2 find the no

Answer 1

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Let the numerator be x

Thus, the denominator will be x + 8

$= > \frac{x + 17}{x + 8 - 1} = \frac{3}{2} \\ \\ = > \frac{x + 17}{x + 7} = \frac{3}{2} \\ \\ = > 2(x + 17) = 3(x + 7) \\ \\ = > 2x + 34 = 3x + 21 \\ \\ = > 34 - 21 = 3x - 2x \\ \\ = > x = 13 \\ \\ = > \frac{13}{13 + 8} = \frac{13}{21}$

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Answer 2

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