I made a clumsy calculation mistake and got it wrong. However I want to verify my reasoning.
Ca = concetration of chemical A
Cb = concetration of chemical B
rate = k (Ca ^2)
rate = k' (1/ Cb)

Now if the Cb is increased by 100% i.e it is doubled, the rate becomes half.
To maintain the rate constant it has to be multiplied by a factor of 2 . So the concentration of A has to be increased as it is directly proprtional . A, B, C are out.
40% increase means new conc of A is 1.4 Ca. Squaring it is 1.96 Ca ~ 2 Ca hence doubled.
50% increase means teh new con of A is 1.5 Ca . Squaring it will give 2.25 Cb which is less approximate than the D option.

Hence D.