The annual rate of growth in population of a town is 10%. If its prese

1.	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» 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.

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»

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.