Multiple choice

In a wildlife sanctuary, the total number of herbivores and carnivores increased by 50% from the year 2000 to 2010. During this period, the herbivore population grew by 80%, while the carnivore population increased by 40%. From 2010 to 2020, the carnivore population further increased by 25%. If in the year 2020, the number of carnivores was three times the number of herbivores, what was the percentage increase in the combined animal population from 2000 to 2020?

  1. 45%

  2. 54%

  3. 75%

  4. 82%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let H and C be initial populations. Total = H+C. 2010: H' = 1.8H, C' = 1.4C. Total' = 1.5(H+C). 1.8H + 1.4C = 1.5H + 1.5C => 0.3H = 0.1C => C = 3H. In 2020, C'' = 1.25 * 1.4C = 1.75C = 1.75(3H) = 5.25H. Given C'' = 3H'', so 5.25H = 3H'' => H'' = 1.75H. Total 2020 = H'' + C'' = 1.75H + 5.25H = 7H. Initial total = H+3H = 4H. Increase = (7H-4H)/4H = 3/4 = 75%.

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