Reaction: 2A+B⟶A2B
Rate =C[A]2[B];C→ rate constant
let conc. of A be a0& that of B be b0 ⇒ Rate =ca02b0=k (say) Aum to question, is concenctration of a is doubled & b is halved ⇒[A]=2a0&[B]=b0/2. ⇒ Rate =c(2a0)2(b0/2) =2a02b0c=2k. ⇒ on doing the following changes as said in question, rate of reaction doubles.