The population of a village is 5500. If the number of males increases by 11% and the number of females increases by 20%, then the population becomes 6330. Find the population of females in the town.
Question
The population of a village is 5500. If the number of males increases by 11% and the number of females increases by 20%, then the population becomes 6330. Find the population of females in the town.
Solution
Let's denote the number of males in the village as M and the number of females as F. We know from the problem that:
M + F = 5500 (equation 1)
After the increase, the number of males becomes M + 0.11M = 1.11M and the number of females becomes F + 0.20F = 1.20F. The total population after the increase is:
1.11M + 1.20F = 6330 (equation 2)
We can solve these two equations to find the values of M and F.
First, let's express M from equation 1:
M = 5500 - F
Now, let's substitute M in equation 2:
1.11(5500 - F) + 1.20F = 6330 6110 - 1.11F + 1.20F = 6330 0.09F = 220 F = 220 / 0.09 F = 2444.44
Since the population must be a whole number, we round this to the nearest whole number, which is 2444.
So, the number of females in the village is approximately 2444.
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