Question

Tick (✓) the correct answer:
The annual rate of growth in population of a town is 10%. If its present population is 33275, what was it 3 years ago?
(a) 25000
(b) 27500
(c) 30000
(d) 26000

Answer 1

(a) 25000

$$\begin{gathered} \mathrm{Let}P\mathrm{be}\mathrm{the}\mathrm{popultion}3\mathrm{years}\mathrm{ago}. \\ \mathrm{Now},\mathrm{present}\mathrm{population}=33275 \\ \Rightarrow 33275=P\times {\left(1+\frac{10}{100}\right)}^3 \\ \Rightarrow 33275=P\times {\left(\frac{110}{100}\right)}^3 \\ \Rightarrow 33275=P\times \left(\frac{11}{10}\right)\times \left(\frac{11}{10}\right)\times \left(\frac{11}{10}\right) \\ \Rightarrow 33275=\frac{1331P}{1000} \\ \therefore P=\frac{33275\times 1000}{1331}=25000 \end{gathered}$$