A wire of resistance R has it length and cross - section both doubled. Its resistance will become:

1R

Wire’s cross section doubled means its cross section area is doubled.

Resistance = (specific resistance ) X (length) / (Area)

Hence, if length and  cross section area both doubled, resistance will remain same i.e inchanged. 

lets say length is L and cros section is A = pi * r ^2

Resistance, R = (roh * L)/ (pi * r^2)

if the length and cross section both are doubled then the resistance is

R2 = (roh *2L)/ (pi*4r^2)

Now R2/R = [(roh *2L)/ (pi*4r^2)] / [(roh * L)/ (pi * r^2)]

then R2 = R /2

so, the resistance will be half of previous.