The population of a village increased every year at the rate of 25%. If it was 10,000 at the end of 3 years, what was the population at the beginning of the first year?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5120
A yearly growth of 25% multiplies the population by \(\frac{125}{100}=\frac{5}{4}\) each year, and the increase each year is on the new, larger population. Going back, the final figure is divided by \(\frac{5}{4}\) three times.
Population after 3 years \(\displaystyle =P\times\frac{5}{4}\times\frac{5}{4}\times\frac{5}{4}=\frac{125P}{64}\)
\(\displaystyle \frac{125P}{64}=10000\)
\(\displaystyle P=\frac{10000\times64}{125}=80\times64=5120\)
The population at the beginning was 5120.