Explanation:
The question is related to the concept of Biochemical Oxygen Demand (BOD) and Dissolved Oxygen (D.O.) in a sewage sample. Let's understand the terms first:

Biochemical Oxygen Demand (BOD):
BOD is the amount of dissolved oxygen required by aerobic microorganisms to break down organic matter (biodegradable substances) present in sewage. It is usually expressed in mg/L (milligrams per liter).

Dissolved Oxygen (D.O.):
D.O. is the amount of oxygen dissolved in water. It is necessary for aquatic life to survive. It is also expressed in mg/L.

Now, coming to the question, it says that the D.O. of a sewage sample is equal to the total oxygen required to satisfy its BOD. This means that all the available dissolved oxygen in the sewage is being consumed by the microorganisms to degrade the organic matter. In other words, the sewage is completely depleted of dissolved oxygen.

So, what does the relative stability of the sewage sample mean here? It refers to the ability of the sewage sample to sustain the aerobic microorganisms that are responsible for biodegradation.

If the D.O. of the sewage sample is zero, it means that the aerobic microorganisms cannot survive and the sewage is in a state of complete instability. However, in this case, the D.O. is equal to the BOD, which means that the microorganisms are able to survive and degrade the organic matter, but there is no excess oxygen available in the sewage.

Therefore, the sewage sample is 100% stable. It can sustain the aerobic microorganisms and continue the process of biodegradation without any additional oxygen supply.

Hence, option (c) 100% is the correct answer.