Option C is correct.
slotted Aloha - Time is divided in slots, so, either A or B transmits only at beginning of a slot.
Given, A's probability to transmit = p
Let B's probability to transmit = x
So, probability of unsuccessful transmission = probability that both A & B transmit = x * p
probability of successful transmission by A = P(A) - P(A∩B) = p - xp
probability of successful transmission by B = P(B) - P(A∩B) = x - xp
Now, since B should have twice the throughput of A, this gives
x - xp = 2* (p - xp)
=> x + xp = 2p
=> x= 2p/ (1+p) Option C (Ans).