Question
The population of a city in 2018 was (x + 5000). It increased by 15% in the first year and by 10% in the second year. The population in 2020 became (x + 8445). Find the population of the city if instead it had increased by 20% in the first year and then decreased by 15% in the second year.
Solution
ATQ, (x + 5000) * 115/100 * 110/100 = x + 8445 (x + 5000) * 1.265 = x + 8445 1.265x + 6325 = x + 8445 1.265x – x = 8445 – 6325 0.265x = 2120 x = 8000 Initial population in 2018 = x + 5000 = 8000 + 5000 = 13000 Now, if population had increased by 20% in the first year and decreased by 15% in the second year: New population = (8000 + 5000) * 120/100 * 85/100 = 13000 * 1.2 * 0.85 = 13000 * 1.02 = 13260 So, the new population of the city = 13260
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