The population of a village was 9800. In a year, with the tomase In population of males by 8% and that of females by 5%, the pop ulation of the village became 10458, What was the number of males in the village before in crease?

Options

A. 4200
B. 4410
C. 5600
D. 6048

Answer

To solve the problem, we need to find the number of males in the village before the increase in population. Let's break it down step by step.

### Step 1: Understand the given data
- Initial population of the village = 9800
- New population after the increase = 10458
- Increase in the population of males = 8%
- Increase in the population of females = 5%

### Step 2: Calculate the total increase in population
To find the total increase in population, we subtract the initial population from the new population.

\[ \text{Increase in population} = \text{New population} - \text{Initial population} \]
\[ \text{Increase in population} = 10458 - 9800 = 658 \]

### Step 3: Define the variables
Let:
- \( M \) = number of males in the village before the increase
- \( F \) = number of females in the village before the increase

From the initial population, we have:
\[ M + F = 9800 \quad \text{(1)} \]

### Step 4: Calculate the increase in males and females
The increase in males and females can be expressed as:
- Increase in males = \( 0.08M \)
- Increase in females = \( 0.05F \)

The total increase in population can also be expressed as the sum of the increases in males and females:
\[ 0.08M + 0.05F = 658 \quad \text{(2)} \]

### Step 5: Solve the equations
Now we have two equations:
1. \( M + F = 9800 \)
2. \( 0.08M + 0.05F = 658 \)

From equation (1), we can express \( F \) in terms of \( M \):
\[ F = 9800 - M \quad \text{(3)} \]

Substituting equation (3) into equation (2):
\[ 0.08M + 0.05(9800 - M) = 658 \]
Expanding this:
\[ 0.08M + 490 - 0.05M = 658 \]
Combining like terms:
\[ 0.03M + 490 = 658 \]
Subtracting 490 from both sides:
\[ 0.03M = 168 \]
Dividing by 0.03:
\[ M = \frac{168}{0.03} = 5600 \]

### Step 6: Conclusion
The number of males in the village before the increase was **5600**.

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