Correct answer is: a) 800 hens

Explanation

A poultry farm has provision of food for 200 days.
After 40 days the remaining days are =\left(200-40\right)
\rightarrow 160 days.
Now,
160 days feeding will be provided for 4000 hens
\therefore 1 days feeding will be provided for =\left(4000\times160\right) hens
\therefore 200 days feeding will be provided for =\large\left(\frac{4000\times160}{200}\right) hens
\rightarrow 3200 hens
\therefore The number of hens must be sold =\left(4000-3200\right)
\rightarrow 800 hens.
Ans: 800 hens must be sold after 40 days.

Another way, Rules of Three Method

Here, Days and Hens are Inversely Proportional.
\therefore\;200\;:\;160\;:\;:\;4000\;:\;x
\rightarrow\large\frac{200}{160}=\frac{4000}{x}
\rightarrow 200x=4000\times160
\rightarrow x=\large\frac{4000\times160}{200}
\rightarrow x=3200 hens
\therefore The number of hens must be sold =\left(4000-3200\right)
\rightarrow 800 hens.
Ans: 800 hens must be sold after 40 days so that the remaining food may last for 200 days more for the remaining hens.

Alternative phrasings for this particular math query are:

1. If a poultry farm with 4000 hens has food provisions for 200 days, how many hens should be sold after 40 days to ensure the remaining food lasts for an additional 200 days for the remaining hens?
2. How many hens should be sold after 40 days to extend the remaining food provisions for 200 more days for the remaining hens, given that the poultry farm initially has 4000 hens and food for 200 days?
3. If a poultry farm with 4000 hens has enough food for 200 days, how many hens should be sold after 40 days to ensure the remaining food lasts for an additional 200 days for the remaining hens?