A task is completed in a unique manner: on the first day, one man works; on the second day, two men work; on the third day, three men work, and so on, until the task is finished in 15 days. The same task is then assigned to women, who are known to be 40% as efficient as men. Following the same pattern, calculate the number of days required for the women to complete the task. (Round up to the nearest integer.)

It is said that the task was finished in 15 days, so if we assume that one man does one unit of work each day, the amount of work done by the men after n days can be found by the formula, $$\frac{n\left(n+1\right)}{2}$$

It is given that it takes them 15 days, substituting 15 for n in that formula, we get 120 units of work. 

Now these 120 units are work done by men, it is given that women are 40% less efficient, that means $$0.4\left(M\right)=W$$
The same 120 units of men's work are equivalent to $$\frac{120}{0.4}=300\ units$$ of Women's work. 

From the options we see, 24 days, which will equal $$\frac{24\left(25\right)}{2}=300$$
Hence, the answer is 24.