The population of a city increased at the rate of `20%` every year for the last three years. If the present population is 203904, then what was the population of the city 3 years ago ?

Options

A. 119000
B. 118000
C. 117000
D. 116000

Explanation

To find the population of the city 3 years ago, we can use the formula for calculating the principal amount when we know the final amount, the rate of increase, and the time period.

### Step-by-Step Solution:

1. **Identify the given values:**
- Present population (Amount) = 203904
- Rate of increase = 20%
- Time period = 3 years

2. **Convert the percentage increase into a multiplier:**
- The population increases by 20%, which means it becomes 120% of the previous year's population.
- In decimal form, this is \(1 + \frac{20}{100} = 1.2\).

3. **Set up the formula:**
- The formula to find the population 3 years ago (Principal) is:
\[ \text{Present Population} = \text{Principal} \times (1 + \text{Rate})^{\text{Time}} \]
- Rearranging the formula to find the Principal:
\[ \text{Principal} = \frac{\text{Present Population}}{(1 + \text{Rate})^{\text{Time}}} \]

4. **Substitute the values into the formula:**
- Substitute the values we have:
\[ \text{Principal} = \frac{203904}{(1.2)^3} \]

5. **Calculate \( (1.2)^3 \):**
- Calculate \( (1.2)^3 = 1.2 \times 1.2 \times 1.2 = 1.728 \).

6. **Calculate the Principal:**
- Now substitute back into the formula:
\[ \text{Principal} = \frac{203904}{1.728} \]
- Performing the division:
\[ \text{Principal} \approx 118,000 \]

7. **Conclusion:**
- The population of the city 3 years ago was approximately 118,000.