Explanation:

- A is twice as efficient as B. This means A can do the work twice as fast as B.

- B is thrice as efficient as C. Therefore, B can do the work three times faster than C.

- Together, A, B, and C can complete the work in 5 days. Let's denote the total work as W.

Let's calculate their individual work rates:

- Let C's efficiency be x. Thus, B's efficiency is 3x and A's efficiency is 6x.

- Combined, their efficiency is \(6x + 3x + x = 10x\).

- In 5 days, they finish W, so \(5 \times 10x = W\), which implies \(50x = W\).

Now, using A and C together for 5 days:

- Combined efficiency for A and C is \(6x + x = 7x\).

- Work done by A and C together in 5 days is \(5 \times 7x = 35x\).

Remaining work:

- Remaining work = \(W - 35x = 50x - 35x = 15x\).

B alone can finish the remaining work:

- B's efficiency is \(3x\).

- Time taken by B alone to finish \(15x\) is \(15x / 3x = 5\) days.

Option 2: 5 days is correct.