Question

The population of a village increases by 4 per cent every year. If the present population is 542000 find the population of the village two years ago.

Answer 1

$$\begin{gathered} Dearstudent, \\ Letthepopulationbeforetwoyears=x \\ andPresentpopulation,A=5,42,000 \\ Rateofincrease,r=4\% \\ Time,n=2yrs \\ A=x{\left[1+\frac{R}{100}\right]}^n \\ 5,42,000=x{\left[1+\frac{4}{100}\right]}^2 \\ 5,42,000=x\times \frac{104}{100}\times \frac{104}{100} \\ 5,42,000\times \frac{100}{104}\times \frac{100}{104}=x \\ 5,01,109(approx.)=x \\ thepopulationbeforetwoyearswas5,01,109(approx.) \\ Regards \end{gathered}$$