Question : The population of a town increases by 8% every year. If the present population of the town is 14,580, then what was the population of the town 2 years ago?
Option 1: 13,600
Option 2: 12,200
Option 3: 13,765
Option 4: 12,500
Correct Answer: 12,500
Solution :
Present population = 14580
Increase in population every year = 8%
Let the population of town 2 years ago be $\text{p}$.
Population after 1 year $=\text{p}$ + 8% of $\text{p}=\text{p} + \frac{8}{100}\times{\text{p}}=\text{p}+\frac{2\text{p}}{25} = \frac{27\text{p}}{25}$
After the second-year increase,
Population after 2 years $=\frac{27\text{p}}{25}+\frac{8}{100}\times \frac{27\text{p}}{25} = \frac{27\text{p}}{25}+\frac{54\text{p}}{625}=\frac{675\text{p}+54\text{p}}{625} = \frac{729\text{p}}{625}$
According to the question,
$\frac{729\text{p}}{625}$ = 14580
⇒ $\text{p}=\frac{14580 \times 625}{729} = 20 × 625 = 12500$
$\therefore$ The population of the town 2 years ago was 12,500.
Hence, the correct answer is 12,500.
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