In a town the population increases by 44% in the first year and by 75% in the second year. What is the approximate average annual rate of increase in population over these two years?

Introduction / Context:
This question asks for an average rate of increase when a population grows by different percentages in two consecutive years. In many aptitude exams, such questions expect a simple arithmetic average of the two yearly percentage increases, unless explicitly asking for a compound equivalent rate. Here, the options provided match the simple average approach, which is widely used as an approximate average rate of increase per year when exact compounding is not required.

Given Data / Assumptions:
Population increases by 44 percent in the first year.
Population increases by 75 percent in the second year.
We must find the average annual rate of increase in percentage over two years.
We assume that the question refers to a simple average of the yearly percentage increases, as suggested by the answer choices.

Concept / Approach:
When a question about average percentage increase over multiple years is framed in school level aptitude style and no explicit compounding requirement is mentioned, it usually refers to the arithmetic mean of the individual yearly rates. That is, average rate per year = (rate in year 1 + rate in year 2) / 2. Therefore, we simply add 44 percent and 75 percent, then divide the sum by 2 to obtain the approximate average annual increase. This method is straightforward and matches one of the given options.

Step-by-Step Solution:
Rate of increase in year 1 = 44 percent. Rate of increase in year 2 = 75 percent. Sum of the two percentage increases = 44 + 75. Compute 44 + 75 = 119. Average annual rate of increase = total of rates / number of years. So, average rate per year = 119 / 2. Compute 119 / 2 = 59.5. Therefore, the approximate average annual rate of increase in population is 59.5 percent.

Verification / Alternative check:
If we wanted the exact compound equivalent rate, we could consider a starting population of 100 units. After year 1, population = 100 * 1.44 = 144. After year 2, population = 144 * 1.75 = 252. The overall factor is 100 to 252, or 2.52 times. The compound equivalent annual rate r would satisfy (1 + r)^2 = 2.52, so r is approximately 58.75 percent. This is close to 59.5 percent, and since 58.75 percent is not among the options, the closest and intended answer is the simple average of 59.5 percent.

Why Other Options Are Wrong:
45 percent is far smaller than either of the yearly rates and cannot represent a realistic average of 44 percent and 75 percent. 74 percent and 76 percent are larger than the higher annual increase of 75 percent and cannot be average values. Only 59.5 percent lies between 44 percent and 75 percent and matches the arithmetic mean, which fits the typical exam convention here.

Common Pitfalls:
One common confusion is mixing up simple average rate and compound equivalent rate. Some candidates may try to average the final values rather than the rates. Others may incorrectly attempt to subtract the smaller rate from the larger one or divide the sum by the wrong number of years. To avoid mistakes, clearly identify that this question targets the arithmetic mean of two given percentages and confirm that the result lies between the two original rates.

Final Answer:
The approximate average annual rate of population increase over the two years is 59.5%.