In a village in India, 5% of the people died due to dengue. Of the remaining population, 15% left the village out of fear. If the population after these events is now 3553, what was the population of the village at the beginning?

Introduction / Context:
This problem involves successive percentage decreases on a population. First, a certain percentage of people die, and then a percentage of the survivors leave the village. After both of these reductions, the final population is known. The goal is to reverse these steps and determine the original population before any changes happened. This is a classic reverse percentage problem.

Given Data / Assumptions:

• 5% of the people died due to dengue.
• 15% of the remaining people left the village.
• The final population after both changes is 3553.
• We assume the population counts are whole numbers and that only these two events affected the population.

Concept / Approach:
When a quantity is reduced by a percentage, the remaining part is (100 - percentage)% of the original. When two percentage changes are applied successively, the overall effect is multiplicative. To find the original value from the final value, we divide by the net remaining factor. Here we first calculate the remaining fraction after each step, multiply these to get the overall remaining fraction, and then divide the final population by that fraction to obtain the initial population.

Step-by-Step Solution:
Step 1: Let the initial population be P. Step 2: First, 5% die. So remaining population after deaths = 95% of P = 0.95 * P. Step 3: Next, 15% of the remaining people leave the village. Step 4: Remaining fraction after this second step = 100% - 15% = 85% of the current population. Step 5: Thus, final population = 0.85 * (0.95 * P) = 0.8075 * P. Step 6: We are told final population = 3553, so 0.8075 * P = 3553. Step 7: Solve for P: P = 3553 / 0.8075. Step 8: Carry out the division: 3553 / 0.8075 = 4400. Step 9: Therefore, the initial population of the village was 4400.

Verification / Alternative check:
Start with 4400 and apply the given reductions to confirm. First 5% die: 5% of 4400 = 0.05 * 4400 = 220; remaining = 4400 - 220 = 4180. Next, 15% of 4180 leave: 0.15 * 4180 = 627. Remaining = 4180 - 627 = 3553. This matches the given final population, confirming the calculation is correct.

Why Other Options Are Wrong:
3100 and 2800 are too low; if we apply the same percentage reductions to them, the result is far below 3553.
5600 is too high; after the same successive percentage drops, the final population would exceed 3553 significantly. Only 4400 reproduces the exact final population of 3553 when the given percentages are applied.

Common Pitfalls:
One common mistake is to add the percentages and assume a single 20% reduction (5% + 15%), which is incorrect because the second percentage is applied on a reduced base. Another mistake is trying to work from the beginning rather than from the end; reversing the process by dividing by the net remaining fraction is more straightforward. Also, some learners forget to convert percentages into decimals properly before multiplying or dividing.

Final Answer:
The original population of the village was 4400.