Which one of the following formula is used for calculating the optimum population?

Question

Accepted Answer

The correct formula for calculating optimum population, according to the given answer, is **M = (A-O)/O**. Here's why this formula is presented as correct and why the others are incorrect, based on the assumption that this is the intended formula:

**Explanation of why Option 1 (M = (A-O)/O) is considered correct:**

This formula, if interpreted in a specific context, *could* represent a simplified model for determining the degree of mal-adjustment (M) in a population size. Let's break it down, assuming the variables represent the following:

*   **M:** Degree of Maladjustment (how far the current population is from the optimum)
*   **A:** Actual Population
*   **O:** Optimum Population

In this context, the formula suggests:

1.  **(A - O):** This calculates the difference between the actual population and the optimum population. If A > O, the result is positive, indicating overpopulation. If A < O, the result is negative, indicating underpopulation.
2.  **/ O:** Dividing the difference by the optimum population normalizes the result. This expresses the maladjustment as a proportion of the optimum population.

Therefore, the formula *could* be interpreted as a measure of the proportional deviation of the actual population from the ideal or optimum population. A higher absolute value of 'M' would indicate a greater degree of maladjustment.

**Explanation of why the other options are incorrect:**

*   **Option 2: M = (OA)/A**

This formula simplifies to M = O. This implies that the degree of maladjustment is always equal to the optimum population, which doesn't make logical sense in the context of population studies. The degree of maladjustment should depend on the *difference* between the actual and optimum populations, not just the optimum population itself.

*   **Option 3: A = (M-O)/O**

This formula solves for 'A' (Actual Population) in terms of 'M' (Maladjustment) and 'O' (Optimum Population). While mathematically valid, it's not the standard way to express the relationship for *calculating* optimum population. It's more useful for determining the actual population given the maladjustment and optimum population. Rearranging Option 1 to solve for 'O' would be a more direct approach if the goal was to calculate the optimum population.

*   **Option 4: A = (OM)/M**

This formula simplifies to A = O. This implies that the actual population is always equal to the optimum population, regardless of any other factors. This is clearly not a realistic or useful representation of population dynamics. The actual population can be above or below the optimum.

**In summary:**

While the formula in Option 1 (M = (A-O)/O) might not be a universally recognized or comprehensive formula for determining optimum population in real-world scenarios (which often involve complex economic, social, and environmental factors), it *can* be interpreted as a simplified measure of the proportional deviation from the optimum. The other options are incorrect because they lead to illogical or trivial relationships between the variables.