it is really an interesting as well as challenging problem.
Now one important point is to be kept in mind. As we stretch the wire then its diameter will be reduced and hence area of cross section would decrease. This would increase the resistance of the wire. So just to escape from such a mesh it will be apt to consider the volume which would remain constant ever after stretching
So R = K l / A
Or R = K l2 / V (by multiplying both numerator and denominator by l)
So R = F l2
Here F is some other proportionality constant
Hence Rf/ Rin=[ lf/ lin]2
Rf/Rin = [100.2/100]2 = 1.004
Hence Rf/Rin = 100.4 / 100
Percentage change in resistance will be 0.4 %
