A village loses 12% of its goats in a flood and then 5% of the remaining goats die due to disease.\nIf 8360 goats are still alive after both losses, what was the original number of goats in the village before the flood?

Introduction / Context:
This question deals with successive percentage decreases applied to a population, in this case goats in a village. First a certain percentage of animals are lost in a natural disaster, and then another percentage of the survivors die due to disease. We know the final count and are asked to work backward to the original number. Problems of this type appear under percentage, population growth and decay, and compound change topics, and they develop skill in reversing multi step percentage processes.

Given Data / Assumptions:

• First loss: 12% of the original goats die in a flood.
• Second loss: 5% of the remaining goats die due to disease.
• Number of goats left after both losses = 8360.
• We need to find the original number of goats before the flood.
• There are no other gains or losses besides the two mentioned events.

Concept / Approach:
Successive percentage decreases can be represented by multiplication factors applied to the original quantity. If the village initially has x goats, then after a 12% loss, the number becomes x * (1 - 12 / 100) = x * 0.88. After this, a further loss of 5% occurs, which reduces the number by a factor of (1 - 5 / 100) = 0.95, giving x * 0.88 * 0.95. We know this final value equals 8360. So we solve the equation x * 0.88 * 0.95 = 8360 to find x, the original population.

Step-by-Step Solution:
Step 1: Let the original number of goats be x. Step 2: After the flood, 12% die, so 88% remain. Remaining after flood = 0.88 * x. Step 3: Of these remaining goats, 5% die due to disease, so 95% survive this second event. Step 4: Number of goats after disease = 0.95 * (0.88 * x) = 0.88 * 0.95 * x. Step 5: According to the problem, this final number is 8360, so 0.88 * 0.95 * x = 8360. Step 6: Compute the combined multiplier: 0.88 * 0.95 = 0.836. Step 7: So the equation becomes 0.836 * x = 8360. Step 8: Solve for x: x = 8360 / 0.836. Step 9: 8360 / 0.836 simplifies to 10000, so the original number of goats is 10000.

Verification / Alternative check:
Check the answer by applying the given losses to 10000 goats. First loss of 12% means 12 / 100 * 10000 = 1200 goats die, leaving 10000 - 1200 = 8800 goats. Second loss of 5% of 8800 means 5 / 100 * 8800 = 440 goats die, leaving 8800 - 440 = 8360 goats. This matches the number stated in the question, confirming that our backward calculation is correct and that 10000 goats is indeed the original population before the flood.

Why Other Options Are Wrong:
If the original population were 1000 goats, even with small percentage losses, the final count could never be as high as 8360. A value of 8360 as the original population would lead to a lower final number after the two losses, not the same value. An original population of 1,00,000 goats would result in a final population ten times larger than required. Only 10000 goats leads to exactly 8360 goats after the given successive losses, so the other options are incompatible with the problem data.

Common Pitfalls:
A common mistake is to subtract 12% and 5% directly and treat the total loss as 17% of the original, which ignores that the second loss applies to a reduced base. Another error is to try to work additively instead of multiplicatively, leading to an incorrect equation. Some learners also reverse the process incorrectly, for example by adding 12% and 5% to the final number. Always represent each stage as a multiplier and work systematically either forward or backward.

Final Answer:
The village originally had 10000 goats before the flood and disease losses.