Question

The annual rate of growth in population of a town is 10%. If its present population is 33275, what was it 3 years ago? 

A. Rs. 25000 

B. Rs. 27500 

C. Rs. 30000 

D. Rs. 26000

Answer 1

Let 3 years ago population = P 

Present population = 33275 

Time, n = 3 years 

Increases rate, R = 10% per annum 

Now, 

Amount (A) = P (1 + R/100)ⁿ [Where, A = Amount with compound interest 

P = Present value 

R = Annual interest rate 

n = Time in years] 

∴ Population = P (1 + R/100)ⁿ 

⇒ 33275 = P (1 + 10/100)³ 

⇒ 33275 = P (1 + 1/10)³ 

⇒ 33275 = P (11/10)³ 

⇒ 33275 = P × 1331/1000 

⇒ P = 33275 × 1000/1331 

⇒ P = 25 × 1000 

⇒ P = 25000 

∴ 3 years ago population is 25000.