The population of a city in 2017 increased by `12.5%` from 2016 and in 2018 it decreased by 8% with respect to previous year and in 2019 it again increased by 15% with respect to previous year. If in 2019, the population of the city is 1190250, then what was the population of city in 2016?

Options

A. 900000
B. 1000000
C. 850000
D. 950000

Answer

To find the population of the city in 2016, we will work backward from the population in 2019, applying the percentage changes for each year step by step.

### Step 1: Understand the population in 2019
We know that the population in 2019 is 1,190,250.

### Step 2: Calculate the population for 2018
In 2019, the population increased by 15% compared to 2018.
Let the population in 2018 be \( P_{2018} \).

Using the formula for percentage increase:
\[ P_{2019} = P_{2018} \times \left(1 + \frac{15}{100}\right) \]
This can be rearranged to find \( P_{2018} \):
\[ P_{2018} = \frac{P_{2019}}{1 + \frac{15}{100}} = \frac{1,190,250}{1.15} \]

Calculating \( P_{2018} \):
\[ P_{2018} = \frac{1,190,250}{1.15} = 1,034,500 \]

### Step 3: Calculate the population for 2017
In 2018, the population decreased by 8% compared to 2017.
Let the population in 2017 be \( P_{2017} \).

Using the formula for percentage decrease:
\[ P_{2018} = P_{2017} \times \left(1 - \frac{8}{100}\right) \]
This can be rearranged to find \( P_{2017} \):
\[ P_{2017} = \frac{P_{2018}}{1 - \frac{8}{100}} = \frac{1,034,500}{0.92} \]

Calculating \( P_{2017} \):
\[ P_{2017} = \frac{1,034,500}{0.92} = 1,123,913.04 \approx 1,123,913 \]

### Step 4: Calculate the population for 2016
In 2017, the population increased by 12.5% compared to 2016.
Let the population in 2016 be \( P_{2016} \).

Using the formula for percentage increase:
\[ P_{2017} = P_{2016} \times \left(1 + \frac{12.5}{100}\right) \]
This can be rearranged to find \( P_{2016} \):
\[ P_{2016} = \frac{P_{2017}}{1 + \frac{12.5}{100}} = \frac{1,123,913}{1.125} \]

Calculating \( P_{2016} \):
\[ P_{2016} = \frac{1,123,913}{1.125} = 999,999.78 \approx 1,000,000 \]

### Conclusion
The population of the city in 2016 was approximately **1,000,000**.

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