Question

The denominator of a rational number is grater the 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

let the numereator be x 
therefore acc. to the questions
x+17/x+8-1=3/2
x+17/x+7=3/2
2(x+17)=3(x+7)
2x+34=3x+21
2x-3x=21-34
-x=-13
x=13

Answer 2

Let us assume, x is the numerator and y is the denominator of the rational number. and the rational number = x/y

Given:

y = x + 8 ------------------1

Also given:

(x + 17) / (y - 1) = 3/2
2 (x + 17) = 3 (y - 1)
2x + 34 = 3y - 3
3y - 2x = 37 --------------2

Substitute the value of y from equation 1 in equation 2

3 (x + 8) - 2x = 37
3x + 24 - 2x = 37
x = 37 - 24
x = 13

Therefore, y = x + 8 = 13 + 8 = 21

Therefore, the rational number = x/y = 13/21