An epidemic broke out in a village in which 5% of the population died. Of the remaining, 20% fled out of panic. If the present population is 4655, then the population of the village originally was

Options

A. 6000
B. 6125
C. 5955
D. 5995

Answer

To find the original population of the village before the epidemic and the subsequent fleeing of the people, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the percentage of the population that died:**
- According to the problem, 5% of the population died due to the epidemic. This means that 95% of the population remained.

**Hint:** Remember that if 5% died, the remaining percentage is calculated as 100% - 5%.

2. **Calculate the percentage of the remaining population that fled:**
- Out of the remaining 95%, 20% fled. Therefore, the percentage that stayed is 80% of the remaining population.

**Hint:** To find the percentage that stayed, subtract the percentage that fled from the remaining percentage.

3. **Set up the equation based on the current population:**
- We know that the present population is 4655, which represents 80% of the remaining 95% of the original population. We can express this as:
\[ \text{Present Population} = 80\% \times 95\% \times \text{Original Population} \]
\[ 4655 = 0.80 \times 0.95 \times \text{Original Population} \]

**Hint:** Convert percentages to decimals for calculations (e.g., 80% = 0.80).

4. **Calculate the combined percentage:**
- Calculate \(80\% \times 95\%\):
\[ 0.80 \times 0.95 = 0.76 \]
Thus, we can rewrite the equation as:
\[ 4655 = 0.76 \times \text{Original Population} \]

**Hint:** Multiplying the decimal values gives you the total percentage of the original population that remains.

5. **Solve for the original population:**
- To find the original population, divide both sides of the equation by 0.76:
\[ \text{Original Population} = \frac{4655}{0.76} \]
\[ \text{Original Population} = 6125 \]

**Hint:** When dividing, ensure you perform the operation carefully to avoid mistakes.

### Final Answer:
The original population of the village was **6125**.