Q.Due to an anti-smoking campaign, the number of smokers decreases at a rate of \(6 \cfrac{1}{4}\%\) per year. If there are currently 22,500 smokers in a city, what was the number of smokers in that city 2 years ago?

Assume the number of smokers 2 years ago was \(x\). Given that the number of smokers decreases annually by \(6 \cfrac{1}{4}\%\), we write the current number of smokers as: \[ x \left(1 - \frac{\frac{25}{4}}{100}\right)^2 = x \left(1 - \frac{25}{400}\right)^2 = x \left(1 - \frac{1}{16}\right)^2 = x \left(\frac{15}{16}\right)^2 \] According to the condition: \[ x \times \left(\frac{15}{16}\right)^2 = 22500 \Rightarrow x = \frac{22500 \times 16 \times 16}{15 \times 15} = 25600 \] \[ \therefore \text{The number of smokers 2 years ago was } 25,600. \]
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