In a town, the population was 8000. In one year, male population increased by 10% and female population increased by 8% but the total population increased by 9%. The number of males in the town was:

Options

A. 4000
B. 4500
C. 5000
D. 6000

Answer

To solve the problem step by step, we can use the method of allegation. Here is the detailed solution:

### Step 1: Understand the given data
- Initial total population = 8000
- Male population increase = 10%
- Female population increase = 8%
- Total population increase = 9%

### Step 2: Calculate the new total population
The total population increased by 9%, so we calculate the new total population:
\[ \text{New Total Population} = \text{Old Population} + (\text{Old Population} \times \text{Percentage Increase}) \]
\[ \text{New Total Population} = 8000 + (8000 \times 0.09) = 8000 + 720 = 8720 \]

### Step 3: Set up the allegation method
We will use the allegation method to find the ratio of males to females based on their percentage increases:
- Male increase = 10%
- Female increase = 8%
- Total increase = 9%

We can set this up as follows:
- Place the male increase (10%) at the top,
- Place the female increase (8%) at the bottom,
- Place the total increase (9%) in the middle.

### Step 4: Calculate the differences
Now, we calculate the differences:
- Difference between male increase and total increase: \(10\% - 9\% = 1\%\)
- Difference between total increase and female increase: \(9\% - 8\% = 1\%\)

### Step 5: Set up the ratio
The ratio of males to females can be determined from the differences:
\[ \text{Ratio of males to females} = \frac{\text{Difference (Female)}}{\text{Difference (Male)}} = \frac{1}{1} = 1:1 \]

### Step 6: Calculate the number of males and females
Since the ratio of males to females is 1:1, we can conclude that half of the total population is male and half is female.
\[ \text{Number of Males} = \frac{\text{Total Population}}{2} = \frac{8000}{2} = 4000 \]

### Final Answer
The number of males in the town is **4000**.

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