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The annual rate of growth in population of a certain city is 8 %. If its present population is 196830, what it was 3 years. ago?

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156250

answer is A.

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Detailed Solution

Given,
Present population of a city

= 196830

,
Rate of growth of population, R=8%,
Number of years

, n = 3

.
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 years:
Population after n years

= P 1 + R 100 n

Let the population of a city 3 years ago be P.
Thus,

196830 = P 1 + 8100 3 ⇒ 196830 = P 1.08 3 ⇒ 196830 = P × 1.259712 ⇒ 196830 1.259712 = P ⇒ P = 156250

Hence, the population of a city three years ago was 156250.
Therefore, option (1) is correct.

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