Question : The population of a village decreases at the rate of 40% per annum. If its population 2 years ago was 15,000, then find the present population.
Option 1: 5400
Option 2: 3500
Option 3: 4450
Option 4: 4400
Correct Answer: 5400
Solution :
Given: The population of a village decreases at the rate of 40% per annum. The population 2 years ago was 15,000.
The previous population ($x$) = 15000
The decrease rate ($r$) = 40%
Time ($t$) = 2 years
So, the present population = $x(1-\frac{r}{100})^2$
= $15000(1-\frac{40}{100})^2$
= $15000×\frac{3}{5}×\frac{3}{5}$
= $5400$
Hence, the correct answer is 5400.
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