The population of a town is 15000. If the number of males Increases by 8% and that of females by 10%, then the population would increase to 16300. Find the number of females in the town.

Options

A. 4000
B. 6000
C. 3000
D. 5000

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define Variables
Let the number of males in the town be \( M \) and the number of females be \( F \).

### Step 2: Set Up the Initial Equation
According to the problem, the total population is given by:
\[ M + F = 15000 \]

### Step 3: Determine the Increase in Population
The population after the increase is given as 16300. The increase in population can be calculated as:
\[ 16300 - 15000 = 1300 \]

### Step 4: Express the Increase in Terms of Males and Females
The increase in population is due to an 8% increase in males and a 10% increase in females. This can be expressed as:
\[ 0.08M + 0.10F = 1300 \]

### Step 5: Simplify the Equation
We can rewrite the equation for easier calculations:
\[ 8M + 10F = 130000 \quad \text{(multiplying the entire equation by 100)} \]

### Step 6: Solve the System of Equations
Now we have a system of two equations:
1. \( M + F = 15000 \)
2. \( 8M + 10F = 130000 \)

From the first equation, we can express \( M \) in terms of \( F \):
\[ M = 15000 - F \]

### Step 7: Substitute into the Second Equation
Substituting \( M \) in the second equation:
\[ 8(15000 - F) + 10F = 130000 \]
Expanding this gives:
\[ 120000 - 8F + 10F = 130000 \]
Combining like terms:
\[ 120000 + 2F = 130000 \]

### Step 8: Isolate \( F \)
Now, isolate \( F \):
\[ 2F = 130000 - 120000 \]
\[ 2F = 10000 \]
\[ F = 5000 \]

### Step 9: Conclusion
The number of females in the town is:
\[ \boxed{5000} \]

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