Condition 1: The numerator of a fraction is 4 less than the denominator
Numerator = Denominator - 4
=> x = y - 4
=> y = x + 4 ------------------------- (1)
Condition 2: If 1 is added to both its numerator and denominator, it becomes 1/2
=> (x +1) / (y +1 ) = 1/2
=> 2(x + 1 ) = y + 1 (By cross multiplication)
=> 2x + 2 = y + 1
=> 2x + 2 = x + 4 + 1 (By substituting for 'y' from equation (1))
=> 2x - x = 5 - 2
=> x = 3
Therefore,
y = 3 + 4 = 7 (Back substituting the value value of 'x' in equation (1))
Hence, x = 3, y = 7