Question

The population of a place in a particular year increased by 15 %. Next year it decreased by 15%. Find the net increase or decrease per cent in the initial population.

Answer 1

Answer:

Decreased by 2.25%

Step-by-step explanation:

Let the initial population be x

Find the population after first year:

Increase = 15% of x = 0.15x

Population = x + 0.15x = 1.15x

Find the population after second year:

Decrease = 15% of 1.15x = 0.15(1.15x) = 0.1725x

Population = 1.15x - 0.1725x =  0.9775x

Find the net decrease:

net decrease = x - 0.9775x = 0.0225x

Find the percentage decrease:

Percentage decrease = (decrease ÷ original) x 100

Percentage decrease = (0.0225x ÷ x) x 100 = 2.25%

Answer: The population has decreased by 2.25%

Answer 2

Answer : $\bold{2.25 \%}$


Explanation -

Let the population = 100

First year, it's increased by 15%

100 x 15/100 = 15

100 + 15 = 115 .

So, population of first year is 115.

Second year, it's decreased by 15%

115 x 15/100 = 17.25

115 - 17.25 = 97.75

So, population of second year is 97.75



Finding the Net decrease -

100 - 97.75 = 2.25

Net decrease = 2.25



Finding the percentage of Net decrease -

Percentage = (Net decrease/initial value) x 100

Percentage = (2.25/100) x 100

Percentage = 2.25%


Hence :

$\bold{Answer : 2.25 \%}$