The population of a city was 120000 in the year 2013 . During next year it incresed by 6% but due to an epidemic it decreased by 5% in the following year. What was its population in the year 2015?

Answer

To find the population of the city in the year 2015, we will follow these steps:

### Step 1: Calculate the population for the year 2014 after a 6% increase.
- **Initial Population in 2013**: 120,000
- **Increase Rate**: 6%

Using the formula for population after an increase:
\[ \text{Population}_{2014} = \text{Population}_{2013} \times \left(1 + \frac{\text{Rate}}{100}\right) \]
Substituting the values:
\[ \text{Population}_{2014} = 120,000 \times \left(1 + \frac{6}{100}\right) = 120,000 \times \left(1 + 0.06\right) = 120,000 \times 1.06 \]
Calculating this:
\[ \text{Population}_{2014} = 120,000 \times 1.06 = 127,200 \]

### Step 2: Calculate the population for the year 2015 after a 5% decrease.
- **Population in 2014**: 127,200
- **Decrease Rate**: 5%

Using the formula for population after a decrease:
\[ \text{Population}_{2015} = \text{Population}_{2014} \times \left(1 - \frac{\text{Rate}}{100}\right) \]
Substituting the values:
\[ \text{Population}_{2015} = 127,200 \times \left(1 - \frac{5}{100}\right) = 127,200 \times \left(1 - 0.05\right) = 127,200 \times 0.95 \]
Calculating this:
\[ \text{Population}_{2015} = 127,200 \times 0.95 = 120,840 \]

### Final Answer:
The population of the city in the year 2015 is **120,840**.

---