To calculate the value of BOD (Biochemical Oxygen Demand) of industrial sewage in kg/day, we need to consider the population equivalent and the specific BOD value per person.

Given:
Population Equivalent (PE) = 6000 persons

To determine the BOD value in kg/day, we can use the following formula:

BOD (kg/day) = BOD per person (kg/day/person) x Population Equivalent (PE)

Let's calculate the BOD value:

BOD per person (kg/day/person):
The BOD per person depends on the type of sewage generated. For domestic sewage, the average BOD per person is typically around 0.08 to 0.1 kg/day/person. However, for industrial sewage, the BOD per person can vary significantly depending on the nature and composition of the industrial effluent.

In this case, the specific BOD per person for industrial sewage is not given. Therefore, we cannot calculate the exact value of BOD. However, we can still analyze the given options and determine the closest approximation based on the range of BOD values for industrial sewage.

Options:
a) 480 kg/day
b) 160 kg/day
c) 270 kg/day
d) 100 kg/day

Based on the range of BOD values for industrial sewage, the closest approximation would be option 'A' - 480 kg/day.

It is important to note that the actual BOD value of industrial sewage can vary significantly depending on various factors such as the type of industry, the specific processes involved, and the composition of the effluent. Therefore, the given options should be considered as approximate values rather than exact calculations.