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.

Let numerator of rational number be x
∴Denominator will be x+8
The rational number will be in the form of p/q = x/(x+8)
As per the question,
(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
Numerator → x = 13
Denominator → x+8 = 13+8 = 21
Rational number = 13/21