Explanation:

- P is two times more efficient than Q. This implies P can do work in half the time Q can.

- Let's say Q takes x days to finish the work alone. Hence, P will complete the same work in x/2 days.

- Given that P completes the work 40 days sooner than Q, so x - x/2 = 40. Solving gives x = 80 days.

- P takes x/2 = 40 days alone.

- Together, their combined work rate can be calculated. P’s rate is 1/40 per day, and Q’s rate is 1/80 per day.

- Together their rate is (1/40 + 1/80) = 3/80 of the work per day.

- To complete the entire work, they take 80/3 days which is approximately 27 days after rounding off.

- Thus, the whole number of days taken by them together to complete the work is 27 days.

Option 3 - 27 is correct.