Last year, the population of a town was x and if it increases at the same rate, next year it will be y. the present population of the town is

$$\eqalign{ & {\text{Let the present population of the town be }}P \cr & {\text{Using compound interest formula}} \cr & {\text{Then}}, \cr & P = x\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right] - - - \,\left( i \right) \cr & {\text{And}}\,y = P\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right] \cr & = P \times \frac{P}{x} - - - - \,\left( {ii} \right) \cr & {P^2} = xy; \cr & {\text{Hence}},\,P = \sqrt {xy} \cr} $$