Population of a village is 5000. If there is an increase in male population by `10% and 15%` increase in female population then the population becomes 5600. Find the number of males in the village.

Answer

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

1. **Understand the given information:**
- Initial population of the village = 5000
- Increase in male population = 10%
- Increase in female population = 15%
- New population after increases = 5600

2. **Calculate the total increase in population:**
\[ \text{Total increase} = \text{New population} - \text{Initial population} = 5600 - 5000 = 600 \]

3. **Determine the percentage increase in population:**
\[ \text{Percentage increase} = \left(\frac{\text{Total increase}}{\text{Initial population}}\right) \times 100 = \left(\frac{600}{5000}\right) \times 100 = 12\% \]

4. **Set up the relationship using the percentage increases:**
- Let the number of males be \( M \) and the number of females be \( F \).
- From the problem, we have:
\[ \text{Increase in males} = 10\% \text{ of } M = 0.1M \]
\[ \text{Increase in females} = 15\% \text{ of } F = 0.15F \]

5. **Write the equation for the total increase in population:**
\[ 0.1M + 0.15F = 600 \]

6. **Express the total population in terms of males and females:**
\[ M + F = 5000 \]

7. **Now, we have a system of equations:**
- Equation 1: \( M + F = 5000 \)
- Equation 2: \( 0.1M + 0.15F = 600 \)

8. **From Equation 1, express \( F \) in terms of \( M \):**
\[ F = 5000 - M \]

9. **Substitute \( F \) into Equation 2:**
\[ 0.1M + 0.15(5000 - M) = 600 \]
\[ 0.1M + 750 - 0.15M = 600 \]
\[ -0.05M + 750 = 600 \]

10. **Solve for \( M \):**
\[ -0.05M = 600 - 750 \]
\[ -0.05M = -150 \]
\[ M = \frac{-150}{-0.05} = 3000 \]

11. **Find the number of males in the village:**
\[ \text{Number of males} = 3000 \]

### Final Answer:
The number of males in the village is **3000**.