For a reaction between A and B, the rate of the reaction doubles when the concentration of A is doubled while keeping concentration of B constant. On the other hand, at constant concentration of A, when concentration of B is reduced to half, the rate of the reaction is reduced to one-fourth. What is the order of the reaction?

Correct option is C

When [A] doubles, rate doubles → Order w.r.t. A = 1
When [B] is halved and rate becomes one-fourth:
(12)n=14⇒n=2\left(\frac{1}{2}\right)^n = \frac{1}{4} \Rightarrow n = 2(21​)n=41​⇒n=2
Total order = 1 (A) + 2 (B) = 3