The population of a village has increased annually at the rate of 25%. If at the end of 3 years it is 10000, the population in the beginning of the first year was :

A. 5120

B. 5000

C. 4900

D. 4500

Answer: Option A

Solution(By Examveda Team)

25% = $$\frac{1}{4}$$
\[\begin{gathered} {\text{Initial }}\,\,\,\,\,\,{\text{Final}} \hfill \\ \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5 \hfill \\ \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5 \hfill \\ \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5 \hfill \\ \overline {\,\,\,\,\,\,64\,\,\,\,\,\,\,\,\,\,125\,\,\,} \hfill \\ \end{gathered} \]

⇒ 125 units = 10000
⇒ 1 unit       = 80
⇒ 64 units = 5120
⇒ Population at the beginning of 1^st year = 5120