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The population of village increases at the rate of 6% per annum. There is an additional increase of 2% in the population due to rural development .Therefore the percentage increase in the population after 2 years will be
- a)15.46%
- b)16.64%
- c)14.46%
- d)12.56%
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The population of village increases at the rate of 6% per annum. There...
Answer – 2.16.64% Explanation : Total increase = 6+2 = 8% % increase = 8+8+(8*8/100) = 16+0.64 = 16.64%
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
The population of village increases at the rate of 6% per annum. There...
EXPLANATION: Let the population after 2 years be x
population increases at the rate of =6%
additional increase =2%
total increase =rate increase +additional increase
= 6+2=8%
General growth formula : A = P(1+r)t
A= amount after growth
P= original amount
r= yearly growth amount (Expressed as a decimal)
t= years
therefore: % increase = 8+8+(8×8/100)
= 16(64/100)
= 16 (0.64)
= 16.64%
therefore:16.64%is the correct answer and it is satisfied according to formula. After 2 years the increase in population will be 16.64%.
thank you
population increases at the rate of =6%
additional increase =2%
total increase =rate increase +additional increase
= 6+2=8%
General growth formula : A = P(1+r)t
A= amount after growth
P= original amount
r= yearly growth amount (Expressed as a decimal)
t= years
therefore: % increase = 8+8+(8×8/100)
= 16(64/100)
= 16 (0.64)
= 16.64%
therefore:16.64%is the correct answer and it is satisfied according to formula. After 2 years the increase in population will be 16.64%.
thank you
Community Answer
The population of village increases at the rate of 6% per annum. There...
Given:
- Population of village increases at the rate of 6% per annum
- Additional increase of 2% in the population due to rural development
To find: Percentage increase in the population after 2 years
Solution:
Let the initial population be P.
After 1 year, the population increases by 6%.
So, population after 1 year = P + (6/100)P = (106/100)P
Due to rural development, there is an additional increase of 2% in population.
So, population after 1 year with rural development = (106/100)P + (2/100)(106/100)P
= (106/100)(1 + 0.02)P
= (106/100)(1.02)P
After 2 years, the population will further increase by 6% and 2%.
So, population after 2 years = (106/100)(1.02)P + (6/100)(106/100)(1.02)P
= (106/100)(1.02)(1 + 0.06)P
= (106/100)(1.02)(1.06)P
Percentage increase in population after 2 years = [(106/100)(1.02)(1.06)P - P]/P * 100
= (1.06412 - 1) * 100
= 6.412%
Therefore, the percentage increase in population after 2 years will be 16.64% (6% + 2% + 6.412%).
Hence, option B is the correct answer.
- Population of village increases at the rate of 6% per annum
- Additional increase of 2% in the population due to rural development
To find: Percentage increase in the population after 2 years
Solution:
Let the initial population be P.
After 1 year, the population increases by 6%.
So, population after 1 year = P + (6/100)P = (106/100)P
Due to rural development, there is an additional increase of 2% in population.
So, population after 1 year with rural development = (106/100)P + (2/100)(106/100)P
= (106/100)(1 + 0.02)P
= (106/100)(1.02)P
After 2 years, the population will further increase by 6% and 2%.
So, population after 2 years = (106/100)(1.02)P + (6/100)(106/100)(1.02)P
= (106/100)(1.02)(1 + 0.06)P
= (106/100)(1.02)(1.06)P
Percentage increase in population after 2 years = [(106/100)(1.02)(1.06)P - P]/P * 100
= (1.06412 - 1) * 100
= 6.412%
Therefore, the percentage increase in population after 2 years will be 16.64% (6% + 2% + 6.412%).
Hence, option B is the correct answer.
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The population of village increases at the rate of 6% per annum. There is an additional increase of 2% in the population due to rural development .Therefore the percentage increase in the population after 2 years will bea)15.46%b)16.64%c)14.46%d)12.56%e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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