length of a conducting wire is increased by 100%.what is the change in its resistance

the wire is actually stretched to increase in length. This means change in length casuses a change in cross section as well.

Given:
Let the initial length of wire=l1
Final length of wire after stretching l2 = l1 +(100/100)l1
=2l1

l2/l1 = 2;

Area of initial wire=A1
Area of final wire = A2
Volume of wire remains constant.
l1A1=l2A2
A2=l1A1/l2
As we know that 
R = ρ l/A
R1/ R2 =( l1/A1 )/(l2/A2),
= l1A2/l2A1.
= l1 (l1A1/l2)/l2A1,
R1/R2 = (l1/l2)^2= 0.25; (since l2/l1 = 2)
R2 = 4R1;
(ΔR/R)×100=(R2-R1/R1)×100= 300%
The percentage increase in resistance is 300%.