Percentage Problem: Understanding the Solution

Hi all,

I was wondering if you could help me with the following...

Q. The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?

Ans: 1650 , 1700, 1750, 1800, 1850.

How I would have tackled this was to decrease 810 and the resulting amount by 50% and 50 years until I hit 160. But that's wrong. Here is the solution..

Sol

If the population increases by 50% every 50 years, the population in 1950 was 150% or 3/2 of the 1900 population. How; is it not just a 50% on 1900 so decreasing the value of 1950 by 50% should result in the 1900 figure?

This mean the 1900 population was 2/3 that of the 1950.... and so on. How is that? 2/3 would be 66% would it not?

A layman explanation so I can understand the principle here would be very much appreciated.

Thanks in Advance,

Paul