Explanation:

- Given that A and B together can finish the work in 20 days:

- Combined work rate of A and B: 1/20 of the work per day.

- B and C together can finish it in 24 days:

- Combined work rate of B and C: 1/24 of the work per day.

- A is twice as efficient as C, implying:

- A = 2C in terms of working ability.

- To find B's work rate:

- Assume C's work rate as x. Then A's work rate is 2x.

- A + B = 1/20, hence 2x + B = 1/20.

- B + C = 1/24, hence B + x = 1/24.

- Solving these equations gives us B's work rate:

- Subtract the second from the first: (2x + B) - (B + x) = 1/20 - 1/24

- x = 1/120

- Substitute x = 1/120 into B + x = 1/24 to find B = 1/30.

- B's work rate is 1/30 of the work per day.

- To find time for B to do 40% of the work:

- 40% of work is 0.4 of the total work.

- Time = Work / Rate = 0.4 / (1/30) = 12 days.

Option:1 - 12 days is correct.