Find the average increase rate if increase in the population in the first year is 30% and that in the second year is 40%.

Options

A. 41
B. 56
C. 40
D. 38

Answer

To find the average increase rate of the population over two years, given that the increase in the first year is 30% and in the second year is 40%, we can follow these steps:

### Step 1: Understand the formula for average increase rate
To find the average increase rate when dealing with percentages over multiple years, we can use the formula:
\[ \text{Average Increase Rate} = \frac{A + B + \frac{A \times B}{100}}{n} \]
where \(A\) is the percentage increase in the first year, \(B\) is the percentage increase in the second year, and \(n\) is the number of years.

### Step 2: Substitute the values into the formula
Here, \(A = 30\%\) and \(B = 40\%\). We have:
\[ \text{Average Increase Rate} = \frac{30 + 40 + \frac{30 \times 40}{100}}{2} \]

### Step 3: Calculate the product of the percentages
Now, calculate \(30 \times 40\):
\[ 30 \times 40 = 1200 \]
Then divide by 100:
\[ \frac{1200}{100} = 12 \]

### Step 4: Add the values together
Now, substitute back into the formula:
\[ \text{Average Increase Rate} = \frac{30 + 40 + 12}{2} \]
Calculating the sum:
\[ 30 + 40 + 12 = 82 \]

### Step 5: Divide by the number of years
Now, divide by the number of years (which is 2):
\[ \text{Average Increase Rate} = \frac{82}{2} = 41 \]

### Final Answer
The average increase rate over the two years is **41%**.