Let the numerator be x and the denominator be y
Sum of numerator and denominator = x + y
Given x + y is 3 less than twice the denominator
So,
=> x + y = 2y - 3
=> x - y +3 = 0 ...(1)
Also, if numerator and denominator are decreased by 1, The numerator becomes half of the denominator
=>(x-1) = 1/2(y-1)
2x - 2 = y – 1
2x - y =2 -1 =1
2x - y = 1 ....(2)
Subtracting (2) and (1) gives x - y + 3 - (2x - y - 1) = 0
x - y + 3 – 2x + y + 1 = 0
-x + 4 =0
x = 4
Substituting x value in (1) gives 4 - y + 3 = 0
y = 7
Therefore x = 4 and y = 7;