For this case we must propose a rule of three:
20 people ----------------> 24 days
32 people ----------------> x
Where the variable "x" represents the number of days it takes 32 people to build the barn.
[tex]x = \frac {32 * 24} {20}\\x = \frac {768} {20}\\x = 38.4[/tex]
Thus, it takes 32 people approximately 39 days to build the barn.
Answer:
It takes 32 people about 39 days to build the barn.
