Question

The average sewage from a city is 90 million litres per day and the average 5-day Biochemical Oxygen Demand (BOD₅) is 300 mg/l. Average standard BOD₅ of the domestic sewage is 0.08 kg/day/person. The population equivalent of the city is

• A. 337500
• B. 216000
• C. 270000
• D. 168750

Hint:

Find the total BOD load (concentration times flow, unit-converted to kg/day), then divide by the standard per-person BOD load.

Answer 1

The Correct Option is A

Step 1: Understand what "population equivalent" means.
Population equivalent (P.E.) converts the organic strength of a wastewater (its BOD load) into the number of people that would produce the same BOD load through domestic sewage alone. It lets an engineer compare an industrial or mixed effluent's pollution load with an equivalent population size.

Step 2: Write the key formula.
\[ \text{Population Equivalent} = \frac{\text{Total BOD load of the sewage (kg/day)}}{\text{Standard BOD load per person (kg/day/person)}} \]
So first we need the total \(BOD_5\) load contributed by the city's sewage in kg per day.

Step 3: Convert the flow to consistent units.
Flow \(Q = 90\) million litres per day (MLD). Since 1 million litres \(= 1000\) m\(^3\),
\[ Q = 90 \times 1000 = 90{,}000 \text{ m}^3/\text{day} \]

Step 4: Convert the concentration to consistent units.
\(BOD_5\) concentration \(C = 300\) mg/l. Since 1 mg/l is numerically the same as 1 g/m\(^3\),
\[ C = 300 \text{ g/m}^3 \]

Step 5: Compute the total BOD load.
\[ \text{Load} = C \times Q = 300 \text{ g/m}^3 \times 90{,}000 \text{ m}^3/\text{day} = 27{,}000{,}000 \text{ g/day} \]
Converting grams to kilograms (divide by 1000):
\[ \text{Load} = 27{,}000 \text{ kg/day} \]

Step 6: Divide by the standard per-person BOD load.
\[ \text{Population Equivalent} = \frac{27{,}000}{0.08} = 337{,}500 \]

Step 7: Rule out the other options.
Option (D) 168750 is exactly half of the correct value, the kind of error you get from mixing up a factor of 2 somewhere in the unit conversion.
Option (B) 216000 and Option (C) 270000 both come from using a wrong load figure rather than the actual 27,000 kg/day BOD load.

Final Answer:
The population equivalent of the city is 337500, option (A).
\[ \boxed{P.E. = 337{,}500} \]