Question

Village $\mathrm{X}$ has a population of $68000$ which is decreasing at the rate of $1200$ per year. Village $\mathrm{Y}$ has a population of $42000$, which is increasing at the rate of 800 per year. In how many years will the population of two villages be equal?

Answer 1

Let the numbers of years be $x$.

For village $\mathrm{X}$, Initial population is $68000$

Decrease in one year$=1200$

Decrease in $x$ years$=1200x$

For village $\mathrm{Y}$, Initial population is $42000$

Increase in one year$=800$

Increase in $x$ year$=800x$

When both villages have same population, then

$$\begin{gathered} 68000–1200\mathrm{x}=42000+800\mathrm{x} \\ \Rightarrow 2000\mathrm{x}=26000 \\ \Rightarrow \mathrm{x}=\frac{26000}{2000} \\ \Rightarrow \mathrm{x}=13 \end{gathered}$$

Therefore, the population of both the villages will be equal in $13\mathrm{years}$.