Ninety-six percent of the population of a village is 23,040. What is the total population of the village?

Introduction / Context:
This is a classic reverse percentage question. Instead of finding a percentage of a known total, we are given a percentage value itself and asked to reconstruct the original total. Such questions appear frequently in exams involving population growth, discounts, profit and loss, and other real life situations where only a part of the whole is known.

Given Data / Assumptions:

96% of the total population equals 23,040.
We need to find the original total population of the village.
Percent values are simple, and no growth over time is involved, only a direct percentage relationship.

Concept / Approach:
Let the total population be P. According to the question, 96% of P is 23,040. In equation form this is:
0.96 * P = 23,040 To find P, we simply divide 23,040 by 0.96. This is the standard way to work backwards from a percentage of a total to the original total.

Step-by-Step Solution:
Step 1: Let total population be P. Step 2: Use the given condition: 96% of P = 23,040. Step 3: Write this in decimal form: 0.96 * P = 23,040. Step 4: Divide both sides by 0.96 to isolate P. P = 23,040 / 0.96. Step 5: Perform the division. 23,040 / 0.96 = 24,000. Step 6: Therefore, the total population of the village is 24,000.

Verification / Alternative check:
To verify, compute 96% of 24,000 and see whether it matches the given figure 23,040. Calculate (96 / 100) * 24,000 = 0.96 * 24,000. Multiplying 24,000 by 0.96 gives 23,040, which is exactly the value given in the question. This confirms that our calculation of the total population is correct.

Why Other Options Are Wrong:
If the population were 32,256, then 96% would be much larger than 23,040.
25,478 and 26,587 both give 96% values that do not match 23,040 when calculated.
23,800 is less than 23,040 when 96% is taken, which is impossible since 96% of a number cannot exceed the number itself.

Common Pitfalls:
Some learners mistakenly compute 23,040 * 0.96 again, which goes in the wrong direction and produces a much smaller number. Another common mistake is to divide by 96 instead of 0.96, forgetting that the percentage must be converted to its decimal form before division. It is also important not to confuse 96% of P with 4% of P, which corresponds to the missing portion of the population in other types of questions.

Final Answer:
The total population of the village is 24,000 people.