Question

In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning

Answer 1

1. let initial population is x
1 st year population increase = 10%
10 % increase in population = 10/100x = 0.1x
after 1 st year population = x+0.1x = 1.1x
after 2n d 10% decrease mean 90 % of the 1st year population = (90÷100)* 1.1x
= 0.99x
at the end of 2nd year population was = 7920
hence 0.99x= 7920
x = 7920÷ 0.99
,x= 792000÷99
,x= 8000



2. another mathod when a value x % increase and y % decrease in consecutive manner
over all decrease or increase in % = x-y-{(xy)÷100}
so population increase 10 % and decrease 10%
overall increase or decrease = 10-10-{(10×10)÷100}%
= -1%(negative sign shows decrease )
= new population = 99% of x
= hence after 2nd year population =(99÷100)x
hence , (99÷100)x= 7920
x=79200÷99
x= 8000
initial population is 8000