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The population of a village has increased annually at the rate of 20%. If at the end of 3 years it is 21600, the population in the beginning of the first year?
- a)10000
- b)12500
- c)15000
- d)17500
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The population of a village has increased annually at the rate of 20%....
Answer – b) 12500 Explanation : 21600 = P*(1 + 20/100)^3
Most Upvoted Answer
The population of a village has increased annually at the rate of 20%....
Given:
- Annual growth rate of population = 20%
- Population at the end of 3 years = 21600
To find:
- Population in the beginning of the first year
Solution:
Let the population at the beginning of the first year be x.
After the first year, the population will increase by 20% and become:
x + 0.2x = 1.2x
After the second year, the population will increase by 20% again and become:
1.2x + 0.2(1.2x) = 1.44x
After the third year, the population will increase by 20% again and become:
1.44x + 0.2(1.44x) = 1.728x
According to the question, this final population value is given as 21600. So:
1.728x = 21600
Solving for x:
x = 12500
Therefore, the population in the beginning of the first year was 12500.
Answer: Option B.
- Annual growth rate of population = 20%
- Population at the end of 3 years = 21600
To find:
- Population in the beginning of the first year
Solution:
Let the population at the beginning of the first year be x.
After the first year, the population will increase by 20% and become:
x + 0.2x = 1.2x
After the second year, the population will increase by 20% again and become:
1.2x + 0.2(1.2x) = 1.44x
After the third year, the population will increase by 20% again and become:
1.44x + 0.2(1.44x) = 1.728x
According to the question, this final population value is given as 21600. So:
1.728x = 21600
Solving for x:
x = 12500
Therefore, the population in the beginning of the first year was 12500.
Answer: Option B.
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Community Answer
The population of a village has increased annually at the rate of 20%....
We can use the formula for compound growth to find the initial population:
where:
- P is the final population (21600)
- P0 is the initial population (what we want to find)
- r is the annual growth rate (20% or 0.20)
- n is the number of years (3)
Plug in the known values:
Simplify and solve for P0:
Simplify and solve for P0:
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