Due to some crisis, Some people from State A migrate to State B, and thereby the population of the second State increased by 19.86%. However, at a later stage, all of them returned to State A. Then by what percentage (correct up to two decimal places) did the population of state B decrease?

Options

A. 19.96
B. 16.64
C. 18.24
D. 17.54

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the initial population of State B
Let the initial population of State B be represented as \( B \).

### Step 2: Calculate the new population after migration
When some people migrate from State A to State B, the population of State B increases by 19.86%. Therefore, the new population of State B can be calculated as:
\[ \text{New Population of State B} = B + (19.86\% \text{ of } B) = B + 0.1986B = 1.1986B \]

### Step 3: Determine the population decrease when people return to State A
When all the migrants return to State A, the population of State B returns to its original number \( B \). The decrease in population can be calculated as:
\[ \text{Decrease in Population} = \text{New Population} - \text{Original Population} = 1.1986B - B = 0.1986B \]

### Step 4: Calculate the percentage decrease in population
To find the percentage decrease in the population of State B, we use the formula:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease in Population}}{\text{New Population}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Decrease} = \left( \frac{0.1986B}{1.1986B} \right) \times 100 \]
The \( B \) cancels out:
\[ \text{Percentage Decrease} = \left( \frac{0.1986}{1.1986} \right) \times 100 \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \text{Percentage Decrease} = \left( 0.1656 \right) \times 100 \approx 16.64\% \]

### Final Answer
Thus, the population of State B decreased by approximately **16.64%**.

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