R proportional to [A]^2
R proportional to 1/
R proportional to [A]^2/
B increased by 100%, therefore B becomes 2B
R is now proportional to [A]^2/2
to keep it proportional to [A]^2/ Numerator should become twice too. Or, A should become sqrt(2)A
sqrt(2)A ~ 1.4A
Or A should approx increase by 40%