Choose the correct option. Population of a village is eight thousand. If 6% men and 10% women are added, population becomes 8600, then the number of men in the village was: Options 4800 5000 5060 6000
Question
Choose the correct option. Population of a village is eight thousand. If 6% men and 10% women are added, population becomes 8600, then the number of men in the village was: Options
4800
5000
5060
6000
Solution
Let's solve this step by step:
- The initial population of the village is 8000.
- The population increases by 600 to become 8600.
- This increase is due to a 6% increase in the number of men and a 10% increase in the number of women.
- Let's assume the number of men in the village is 'x'. Therefore, the number of women in the village would be '8000 - x'.
- According to the problem, 6% of 'x' (the number of men) plus 10% of '8000 - x' (the number of women) equals the increase in population, which is 600.
- We can set up the equation as follows: 0.06x + 0.10(8000 - x) = 600
- Solving this equation will give us the number of men in the village.
Let's solve the equation:
0.06x + 800 - 0.10x = 600 -0.04x = -200 x = 5000
So, the correct option is 5000. There were 5000 men in the village.
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