The population of a town is 6000. If the number of males increase by 8% and the number of females increase by 10%, the population will be 6500. Find the number of females in the town -

Correct option is A

To solve this problem, let's denote the number of males in the town as M and the number of females as F.
Given:
1. The total population of the town = 6000
2. Population after the increase = 6500
3. Percentage increase in the number of males = 8%
4. Percentage increase in the number of females = 10%
Formulas Used:
1. M + F = 6000
2. 1.08M + 1.10F = 6500
Solution:
We have the following two equations:
1. M + F = 6000 --- (1)
2. 1.08M + 1.10F = 6500 --- (2)
From equation (1), we can express M as:
M = 6000 - F
Substitute this into equation (2):
1.08(6000 - F) + 1.10F = 6500
Expanding and simplifying:
1.08 × 6000 - 1.08F + 1.10F = 6500
6480 + 0.02F = 6500
0.02F = 6500 - 6480
0.02F = 20
Solving for F:
F = 20/0.02 = 1000
Thus, the number of females in the town is 1000.