5% population of a town died of some epidemic and 8% of the remaining population left in panic. If the population of the town now is 88,274, find the population of the town at the beginning.

Options

A. `99,800`
B. `1,21,600`
C. `1,01,000`
D. `84,500`

Answer

To find the initial population of the town before the epidemic and the panic, we can follow these steps:

### Step 1: Let the initial population be \( P \).

### Step 2: Calculate the population after 5% died from the epidemic.
- If 5% of the population died, then 95% of the population remains.
- The remaining population after the epidemic is:
\[ \text{Remaining population} = P - 0.05P = 0.95P \]

### Step 3: Calculate the population after 8% left in panic.
- After the epidemic, 8% of the remaining population left in panic, which means 92% of the remaining population stayed.
- The population after the panic is:
\[ \text{Population after panic} = 0.95P \times 0.92 = 0.874P \]

### Step 4: Set up the equation with the current population.
- We know that the current population is 88,274, so we can set up the equation:
\[ 0.874P = 88,274 \]

### Step 5: Solve for \( P \).
- To find \( P \), divide both sides of the equation by 0.874:
\[ P = \frac{88,274}{0.874} \approx 101,000 \]

### Conclusion:
- The initial population of the town was approximately **101,000**.