P is 50% more efficient than Q. Q takes 30 days to complete a certain task alone. P and Q started working together and worked for 8 days. After 8 days, R joined them and the three of them together finished the remaining work in 2 days. In how many days can R alone complete the entire task?

ATQ,
Let Q's 1-day work be q.
Q takes 30 days to complete the work.
So,
q = 1/30.
P is 50% more efficient than Q.
So,
P's 1-day work (p) = 1.
5 × 1/30.
Or,
p = 15/300 = 1/20.
Work done by P and Q together in 8 days = 8(p + q).
Or,
Work done = 8(1/20 + 1/30).
Or,
Work done = 8(3/60 + 2/60) = 8(5/60) = 8/12 = 2/3.
Remaining work = 1 - 2/3 = 1/3.
P,
Q and R together finish the remaining work in 2 days.
So,
2(p + q + r) = 1/3.
Or,
2(1/20 + 1/30 + r) = 1/3.
Or,
2(5/60 + r) = 1/3.
Or,
1/6 + 2r = 1/3.
Or,
2r = 1/3 - 1/6.
So,
2r = 1/6.
So,
r = 1/12.
Hence,
the correct answer is B.