Question

The population of a town was 19,000 in year 2006 and 22,000 in year 2007. Find the percentage
increase in the population in a year.​

Answer 1

Given :

• Population of the town in year 2006 = 19,000.

• Population of the town in year 2007 = 22,000

To find :

Percentage increase in the population of the town.

Solution :

We know the formula for Percentage increase I.e,

$\boxed{\bf{P\% = \bigg(\dfrac{Increase\:in\:Population}{Orginal\:Population} \times 100\bigg)\%}}$

$\boxed{\begin{minipage}{7 cm} \underline{\bf{Population\:Increase}} \\ \\ :\implies \bf{P_{increase} = P_{final} - P_{Intial}} \\ \\ Here , \\ \bullet\: P_{initial} = 19,000 \\ \bullet\: P_{final} = 22,000 \\ \\ :\implies \bf{P_{increase} = 22000 - 19000} \\ \\ :\implies \bf{P_{increase} = 3000} \\ \\ \textsf{Hence the Increase in Population is 3000} \end{minipage}}$

Now using the formula for Percentage increase and substituting the values in it , we get :

$:\implies \bf{P\% = \bigg(\dfrac{3000}{19000} \times 100\bigg)\%}$

$:\implies \bf{P\% = \bigg(\dfrac{3}{19} \times 100\bigg)\%}$

$:\implies \bf{P\% = \bigg(\dfrac{300}{19}\bigg)\%}$

$:\implies \bf{P\% = 16(approx.)\%}$

$\boxed{\therefore \bf{P\% = 16\%}}$

Hence the percentage increase in the population is 16 %.

Answer 2

• GIVEN:-

In 2006 population of the town was 19,000

In 2007 population of the town was 22,000

• To Find:-

Percentage increase in population in a year.

• SOLUTION:-

We know that,

$\large\boxed{\tt{ Increase\%= \huge(\large\frac{Increase\: in\: Population}{Original \:population}\large\times100\huge)\large\%}}$

Therefore increase in population = 22000 - 19000 = 3000

Putting the values,

$\large\Longrightarrow{\tt{ Increase\%=\huge (\huge\frac{3000}{19000}\large\times100\huge)\large\%}}$

$\large\Longrightarrow{\tt{ Increase\%=\huge(\frac{3}{19}\large\times100\huge)\large\%}}$

$\large\Longrightarrow{\tt{ Increase\%= (0.15\times100)\%}}$

$\large\Longrightarrow{\tt{ Increase\%= 15\%}}$

$\large\purple\therefore\boxed{\tt{\purple{Percentage\: increase\: in\: population\:= \:15\%}}}$