Population of a village increased to 55125 in the year 2010 at the rate of 5% p.a. find in 2008?

If you want to increase an amount x of something by p percent of that amount of something, you have to calculate the sum of x and x * 0.01p. As it is here a compound growth over two years you have to apply this function twice:

let x be the population in 2008
p = 5% ; P = 0.05.

x + 0.05x = x (1 + 0.05) = 1.05x ; Population in 2009
1.05² x = 55125 ; in 2010
Now, isolate x:
x = 55125 / 1.05²
x = 55125 / 1.1025
x = 50000 ; Population in 2008.