Question

the population of state is 20000 it increased by 20% during the first year and 30% during the second year the population after two years will be
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Answer 1

$\sf{\star}$ Given:-

• Population of state = 200000
• Increase in population during 1st year $\sf{(r_1)}$ = 20%
• Increase in population during second year $\sf{(r_2)}$ = 30%

$\sf{\star}$ To Find:-

Population of state after two years

$\sf{\star}$ Assumption:-

Let the population after two years be A

$\sf{\star}$ Solution:-

= $\sf{A = P\bigg(1+\dfrac{r_1}{100}\bigg)\bigg(1+\dfrac{r_2}{100}\bigg)}$

= $\sf{A = 200000\bigg(1+\dfrac{20}{100}\bigg)\bigg(1+\dfrac{30}{100}\bigg)}$

= $\sf{A = 200000\bigg(1+\dfrac{2}{10}\bigg)\bigg(1+\dfrac{3}{10}\bigg)}$

= $\sf{A = 200000\bigg(\dfrac{10+2}{10}\bigg)\bigg(\dfrac{10+3}{10}\bigg)}$

= $\sf{A = 200000\times \dfrac{12}{10}\times\dfrac{13}{10}}$

= $\sf{A = 312000}$

Therefore the population after two years will be 312000.

$\sf{\star}$ Note:-

Here,

A stands for population after 2 years.

P stands for the population given in the question.

$\sf{r_1}$ stands for rate of increase in population during 1st year.

$\sf{r_2}$ stands for rate of increase in population during 2nd year.

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