# 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?

Answer

Verified

329.1k+ views

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.

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.

Last updated date: 31st May 2023

•

Total views: 329.1k

•

Views today: 8.85k

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India