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Q.

There is a continuous growth in population of a village at the rate of $5 %$ per annum. If its present population is 9261 what it was 3 years ago?

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a

8000

b

6110

c

8300

d

8360

answer is A.

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Detailed Solution

Given,
Present population of a village =9261,
Rate of growth of population, R=5%,
If P is the population of a city at the beginning of specific year and R% is its constant growth rate per annum, we use the following formula to calculate the population after n year,
Population after n years

= P 1 + R 100 n

.
Number of year, n=3.
Let the population of a village 3 years ago be P.
Present population of a village,

⇒ 9261 = P 1 + 5100 3 ⇒ 9261 = P 1.05 3 ⇒ 9261 = P × 1.1576 ⇒ P = 9261 1.1576 ⇒ P = 8000.17 ⇒ P ≈ 8000

Hence, the population of a village three years ago was 8000.
Therefore, option (1) is correct.

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