Question

The population of a village was $20,000$ and after $2$ years it become $22050$. What is the rate of increase per annum ?

• A. $10\%$
• B. $8\%$
• C. $5\%$
• D. $6\%$

Answer 1

The correct option is C $5\%$

We know that

Final population $=$ (original population)$\times {(1+\frac{Rate}{100})}^{time}.$.........(i)

Here original population $=20000$,

final population $=22050$,

Time $=2$ yrs,

rate=?

Let the rate $=R$.

Substituting the values of the given parameters in (i),

$20000{(1+\frac{R}{100})}^2=22050$

$\Rightarrow {(1+\frac{R}{100})}^2=\frac{22050}{20000}=1.1025$

$\Rightarrow (1+\frac{R}{100})=\sqrt{1.1025}=1.05$

i.e $R=5\%$

Ans- Option C.