The population of a town is decreasing at a uniform rate of `10%` per annum for the last 3 years. If the present population of the town is 137700, what it was 2 years ago?

Options

A. 152847
B. 160000
C. 170000
D. 163657

Answer

To find the population of the town 2 years ago, we will use the formula for population decrease due to a percentage decline. The population decreases at a uniform rate of 10% per annum.

### Step-by-Step Solution:

1. **Identify the Present Population**:
The current population is given as 137,700.

2. **Understand the Decrease Rate**:
The population decreases by 10% each year. This means that at the end of each year, 90% of the population remains.

3. **Calculate the Population 1 Year Ago**:
Let’s denote the population 1 year ago as P1. Since the population decreases by 10%, we can express this as:
\[ P1 = \frac{\text{Present Population}}{0.90} \]
Substituting the present population:
\[ P1 = \frac{137700}{0.90} = 153000 \]

4. **Calculate the Population 2 Years Ago**:
Now, we will find the population 2 years ago (P2) using the same method:
\[ P2 = \frac{P1}{0.90} \]
Substituting the value of P1:
\[ P2 = \frac{153000}{0.90} = 170000 \]

### Final Answer:
The population of the town 2 years ago was **170,000**.