If $$\Delta $$ is the depth of water in metres, B is the number of days of base period and D is the duty in hectare/cumec, the relationship which holds good, is A. $${\text{D}} = \Delta \frac{{8.64{\text{D}}}}{{\text{B}}}$$ B. $${\text{B}} = \Delta \frac{{8.64{\text{B}}}}{{\text{D}}}$$ C. $${\text{D}} = \frac{{8.64\Delta }}{{\text{B}}}$$ D. $$\Delta = \frac{{8.64{\text{B}}}}{{\text{D}}}$$

The correct answer is $\boxed{\text{C}}$.

The duty is the amount of water that can be applied to a hectare of land in one day. It is calculated by dividing the depth of water by the number of days of the base period. The base period is the time period over which the duty is calculated. It is usually taken to be one year.

The depth of water is the vertical distance from the surface of the water to the bottom of the reservoir. It is measured in metres.

The number of days of the base period is the number of days in the period over which the duty is calculated. It is usually taken to be one year.

Therefore, the relationship between the depth of water, the number of days of the base period, and the duty is:

$$\text{D} = \frac{{8.64\Delta }}{{\text{B}}}$$

where:

• $\text{D}$ is the duty in hectare/cumec
• $\Delta$ is the depth of water in metres
• $\text{B}$ is the number of days of the base period

The other options are incorrect because they do not correctly represent the relationship between the depth of water, the number of days of the base period, and the duty.