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The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is?
Verified Answer
The population of a town increases every year by 2% of the population ...
Lets assume that the initial population was P
now after a year population will be
= P+(2/100)P
=P(102/100)
=1.02P
Similarly after 2 years population will be
=1.02x1.02xP
So after n number of years population will be
=P x (1.02^n)
now this population should be equal to P+40%P, so
1.4P=P x (1.02^n)
1.4=1.02^n
1.02^17=1.02^n
so n=17
that means after 17 years the total increase in the population will be 40% of that of initial population.
This question is part of UPSC exam. View all CA Foundation courses
Most Upvoted Answer
The population of a town increases every year by 2% of the population ...
If we go through assumptions
Let population be 100
100+2%+2%+2%...so on upto we get 140
No.of yrs =17 yrs
Let population be 100
100+2%+2%+2%...so on upto we get 140
No.of yrs =17 yrs
Community Answer
The population of a town increases every year by 2% of the population ...
Problem:
The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is?
Solution:
To find the number of years required for the total increase in population to be 40%, we can set up an equation.
Let's assume the initial population of the town as P.
Step 1: Calculate the population after one year:
The population increases by 2% every year, so after one year, the population will be P + (2/100) * P = P + 0.02P = 1.02P.
Step 2: Calculate the population after two years:
Similarly, after two years, the population will be 1.02P + (2/100) * (1.02P) = 1.02P + 0.0204P = 1.0404P.
Step 3: Calculate the population after three years:
Following the same logic, after three years, the population will be 1.0404P + (2/100) * (1.0404P) = 1.0404P + 0.020808P = 1.061208P.
Step 4: Calculate the population after n years:
After n years, the population will be given by the formula:
P * (1 + 0.02)^n
Step 5: Set up the equation:
We need to find the number of years for which the total increase in population is 40%. This can be represented as:
P * (1 + 0.02)^n - P = 0.40P
Simplifying the equation, we get:
(1 + 0.02)^n - 1 = 0.40
Step 6: Solve the equation:
Using logarithms, we can solve for n:
n * log(1.02) = log(1.40)
n = log(1.40) / log(1.02)
Using a calculator, we find that n ≈ 35.35.
Therefore, the number of years required for the total increase in population to be 40% is approximately 35 years.
The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is?
Solution:
To find the number of years required for the total increase in population to be 40%, we can set up an equation.
Let's assume the initial population of the town as P.
Step 1: Calculate the population after one year:
The population increases by 2% every year, so after one year, the population will be P + (2/100) * P = P + 0.02P = 1.02P.
Step 2: Calculate the population after two years:
Similarly, after two years, the population will be 1.02P + (2/100) * (1.02P) = 1.02P + 0.0204P = 1.0404P.
Step 3: Calculate the population after three years:
Following the same logic, after three years, the population will be 1.0404P + (2/100) * (1.0404P) = 1.0404P + 0.020808P = 1.061208P.
Step 4: Calculate the population after n years:
After n years, the population will be given by the formula:
P * (1 + 0.02)^n
Step 5: Set up the equation:
We need to find the number of years for which the total increase in population is 40%. This can be represented as:
P * (1 + 0.02)^n - P = 0.40P
Simplifying the equation, we get:
(1 + 0.02)^n - 1 = 0.40
Step 6: Solve the equation:
Using logarithms, we can solve for n:
n * log(1.02) = log(1.40)
n = log(1.40) / log(1.02)
Using a calculator, we find that n ≈ 35.35.
Therefore, the number of years required for the total increase in population to be 40% is approximately 35 years.
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The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is?.
The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which total increase of population be 40% is?.
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