The population of vultures in a particular locality is decreases by certain rate of interest (compounded annually). If the current population of vultures be 29160 and the ratio of decrease in population for second year and 3rd year be 10 : 9. What was the population of vultures 3 years ago?

A. 30000

B. 35000

C. 40000

D. 50000

E. Cannot determined

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \frac{{{\text{Decrease in second year}}}}{{{\text{Decrease in third year}}}} \cr & = \frac{{100}}{{\left( {100 - r} \right)}} \cr & = \frac{{10}}{9} \to r = 10\% \cr} $$
Let the population of vultures 3 years ago be P, then
$$\eqalign{ & P \times {\left[ {1 - \left( {\frac{{10}}{{100}}} \right)} \right]^3} = 29160 \cr & \to P = 40000 \cr} $$