Question

# The population of the village was decreasing every year due to migration, poverty and unemployment. The present population of the village is $315,840$. Last year the migration was 4% and the year before last, it was 6%. What was the population of the village 2 years ago?

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Hint: In this question assume any variable be the population of village 2 years ago, then apply the concept that if p% population is decreased from present population say (q), then the present population becomes $\left( {q - \dfrac{p}{{100}}q} \right)$ so, use this concept to reach the solution of the question.

Let the population of the village 2 years ago be x.
Now it is given that the first year it was decreased by 6% due to migration, poverty and unemployment.
So, we have to subtract 6% of x from x, to get the population this year, let the population this year be y.
$\Rightarrow y = x - \dfrac{6}{{100}}x$…………… (1)
Now next year the population of the village which is y now and it is decreased by 4% due to migration, poverty and unemployment, so we have to subtract 4% of y from y, let the population this year be z.
$\Rightarrow z = y - \dfrac{4}{{100}}y$…………… (2)
Now it is also given that the population this year was $315,840$.
$\Rightarrow z = 315,840$
Now from equation (2) we have,
$315,840 = y - \dfrac{4}{{100}}y$
$\Rightarrow 315,840 = y - \dfrac{4}{{100}}y \\ \Rightarrow 315,840 = y - \dfrac{1}{{25}}y \\ \Rightarrow 315,840 = \dfrac{{24}}{{25}}y \\ \Rightarrow y = \dfrac{{315,840 \times 25}}{{24}} = 13,160 \times 25 = 329,000 \\$
Now from equation (1) we have
$329,000 = x - \dfrac{6}{{100}}x \\ \Rightarrow 329,000 = x - \dfrac{3}{{50}}x \\ \Rightarrow 329,000 = \dfrac{{47}}{{50}}x \\ \Rightarrow x = \dfrac{{329,000 \times 50}}{{47}} = 7000 \times 50 = 350,000 \\$
So, the required population of the village 2 years ago is 350,000.

Note: In such types of questions remember that the data given in question is that the present population of the village is $315,840$ and Last year the migration was 4% and the year before last, it was 6% , so let the population of the village 2 years ago be x and this year the population is decreased by 6% and next year the population is decreased by 4% now construct the equations as above according to given information and simplify, we will get the required population 2 years ago.