correct answer is: d) 6 days

Explanation

Food provides 12 men for 20 days
\therefore Food provides 1 man for =\left(20\times12\right) days
\therefore Food provides 40 men for =\large\left(\frac{20\times12}{40}\right) days
\rightarrow 6 days
Ans: If the number of men is 40 then the provides food last for 6 days.

Another way, Rules of Three Method

Here, Men and Days are Inversely Proportional.
\therefore\;40\;:\;12\;:\;:\;20\;:\;x
\rightarrow\large\frac{40}{12}=\frac{20}{x}
\rightarrow 40x=20\times12
\rightarrow x=\large\frac{20\times12}{40}
\rightarrow x=6 days
Ans: The provides food last for 6 days.

Other variants of this particular math question are:

1. If a quantity of food sustains 12 men for 20 days, how many days will it last if the number of men increases to 40?
2. How many days will a quantity of food last for 40 men if it typically lasts 12 men for 20 days?
3. Given that a quantity of food lasts 12 men for 20 days, how long will it last if the number of men consuming it increases to 40?
4. If a quantity of food is sufficient for 12 men for 20 days, how many days will it last for 40 men?