In a certain village, the population was 4,000. In one year the population of male increases by 12% and that of female by 20%, but the total population increases by 15%, find the number of males in the village (initially).1800150025002000
Question
In a certain village, the population was 4,000. In one year the population of male increases by 12% and that of female by 20%, but the total population increases by 15%, find the number of males in the village (initially).1800150025002000
Solution
Let's denote the initial number of males as M and the initial number of females as F. We know that M + F = 4000.
After one year, the population of males increased by 12% and the population of females increased by 20%. The total population increased by 15%. This gives us the equation:
1.12M + 1.2F = 4000 * 1.15
We can simplify this equation to:
1.12M + 1.2(4000 - M) = 4600
Solving this equation for M gives us the initial number of males in the village.
1.12M + 4800 - 1.2M = 4600
-0.08M = -200
M = 2500
So, the initial number of males in the village was 2500.
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