Question

The population of a place increased to 26,000 in the year 2001 at a rate of 4% per annum. Then the population in the year 2000 is

• A. 23,000
• B. 24,000
• C. 25,000
• D. 25,500

Answer 1

The correct option is C

25,000

Let $A_{2000}$ be the population of tha place in 2000.

Let $A_{2001}$ be the population of the place in 2001. Then $A_{2001}$ = 26,000

Let R be the rate(per annum) at which the population increased. Then R = 4%

n = 1 year
Population would be less in 2000 than in the year 2001.
$\therefore A_{2001}=A_{2000}{(1+\frac{R}{100})}^n$
$\Rightarrow 26000=A_{2000}{(1+\frac{4}{100})}^1\Rightarrow 26000=A_{2000}{(1+\frac{1}{25})}^1$
$\Rightarrow 26000=A_{2000}\left(\frac{26}{25}\right)$
$\Rightarrow A_{2000}=\frac{26000\times 25}{26}$
$\Rightarrow A_{2000}=25000$