Question : At present, the number of trees in a village is 52,020. It increases annually at the rate of 2%. What was the number of trees in the village two years ago?
Option 1: 45,000
Option 2: 51,250
Option 3: 50,000
Option 4: 48,000
Correct Answer: 50,000
Solution :
Given,
The present number of trees in a village = 52,020
Annual Increase percentage = 2%
Let the number of trees two years ago be $x$.
⇒ Number of trees one years ago after increase $=x+\frac{2}{100}×x= x+\frac{x}{50}$
One years ago number of trees $=\frac{51x}{50}$
So, the present number of trees $=\frac{51x}{50}+\frac{2}{100}×\frac{51x}{50}$
$=\frac{51x}{50}+\frac{51x}{2500}=\frac{2550x+51x}{2500} =\frac{2601x}{2500}$
According to the question,
$\frac{2601x}{2500}=52020$
⇒ $x=\frac{52020×2500}{2601}$
⇒ $x=20×2500=50,000$
Hence, the correct answer is 50,000.
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