The numerator of a number is smaller than its denominator by 5. If the numerator is increased by 8 and denominator by 6, then the new number becomes 5/7. Find the rational number.
1). -4/3
2). 4/3
3). 1/2
4). -1/9
Let the denominator of rational number be x.
Numerator = (x - 5)
New denominator = (x + 6)
New numerator = (x - 5 + 8) = (x + 3)
Given that, (x + 3)/ (x + 6) = 5/7
⇒ 7x + 21 = 5x + 30
⇒ 2x = 9
⇒ x = 9/2
Original rational number = (x - 5)/x = -(1/2)/(9/2) = -1/9
∴ Answer is -1/9