Question

A population of town increased by 20% during the first year by 25% during the next year and by 44% during the third year. Find the average rate of increase during 3 years.

Answer 1

Soln:-
Let the population be x

For the 1st year
Population=x(1+20/100)^1
=x(6/5)
=6/5 x
For the second year
Population=6/5x (1+25/100)^1
=6/5x (5/4)
=3 /2x
For the third year
Population=3/2x(1+44/100)^1
=3/2x (36/25)
=54/25 x
Increase in population=54/25x - x
=29/25 x
Average increase in population=(29/25 x)/3
=29/75 x
=(29/75x)/x ×100℅
=116/3 ℅=38(2/3)℅

Answer 2

Answer:

38.33%

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Step-by-step explanation:

Initial Population = P

First Year increase = (20/100)P = 0.2P

Population after 1 year = P+0.2P = 1.2P

2nd Year Increase = (25/100)*(1.2P) = 0.3P

Population after 2nd Year = 1.2P+0.3P = 1.5P

3rd Year increase = (44/100)*1.5P = 0.66P

Population after 3 years = 1.5P + 0.66P = 2.16P

Population increased in 3 Years = 2.16P - P = 1.16 P

% age increase in 3 years = (1.16P/P)*100 = 116%

per year increase % = 116/3 = 38.33%