Multiple choice

The present population of a village is 1,15,200.If it increases at the rate of $6\frac {2}{3}$% per annum, find (i) its population after 2 years and (ii) its population 2 years ago

  1. 1,31,072;1,01,250

  2. 1,01,250;1,31,072

  3. 1,22,880;1,08,000

  4. 1,08,000;1,22,880
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A Correct answer
Explanation

Population growth rate is 20/3%. After 2 years: 115200 * (1 + 1/15)^2 = 115200 * (16/15)^2 = 131072. Two years ago: 115200 / (16/15)^2 = 101250.

AI explanation

Convert the rate of 6 2/3% to a fraction, which is 20/3% or 1/15. Using the successive percentage increase formula, the population after 2 years is 115200 multiplied by (1 + 1/15) multiplied by (1 + 1/15), giving 115200 multiplied by 16/15 multiplied by 16/15 to equal 131072. To find the population 2 years ago, divide the present population by this same growth factor: 115200 divided by (16/15 multiplied by 16/15) equals 115200 multiplied by 225/256, which gives 101250. The answers are 131072 and 101250.

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