Question

The population of a village was decreasing every year due to migration, poverty and unemployment. The present population of the village is $3,15,840$. Last year the migration was $4$ and the year before last, it was $6$. What was the population of the village $2$ years ago ?

Answer 1

Let the initial population $2$ years ago be ${}^{\prime }{x}^{\prime }$

Given percentage of migration in first year $=6\%$ of $x$

$\therefore$ Remaining population $94\%ofx=\left(\frac{94x}{100}\right)$

Migration percentage in second year $4\%$ of $\left(\frac{94x}{100}\right)$

Remaining population after 2 years $=96\%of\frac{94x}{100}$

Given $3,15,840=\frac{94\times 96\times x}{100\times 100}$

$x=\frac{315840\times 100\times 100}{94\times 96}$

$=35\times 100\times 100=35,00,000$

$\therefore \text{Initial Population}x=3,50,000$