Question

The population of a city was 1,00,000. Find the growth % if the population of the same city becomes 1,33,100 after 3 years.

• A. 10%
• B. 15%
• C. 20%
• D. 30%

Answer 1

The correct option is A 10%

Present population of city ($P_o$) = 1,00,000
Popoution of city after 3 years ($P$) = 1,33,100
Lets say growth rate be $x$% .
Using formula,
$P_n$ = $P_o$ $(1+\frac{Growth}{100}{)}^3$
$⟹$$1,33,100=1,00,000$ $(1+\frac{x}{100}{)}^3$
$⟹$$1,331=1,000$ $(1+\frac{x}{100}{)}^3$
$⟹$$\frac{1,331}{1,000}$ $=$ $(1+\frac{x}{100}{)}^3$
$⟹$$(\frac{11}{10}{)}^3$ $=$ $(1+\frac{x}{100}{)}^3$
$⟹$ $(1+\frac{1}{10}{)}^3$ $=$ $(1+\frac{x}{100}{)}^3$
Now, we can compare, $\frac{1}{10}$ and $\frac{x}{100}$
Thus, $\frac{1}{10}$ $=$ $\frac{x}{100}$
So, $x$ $=$ 10%