Question
The population of a town increases by 10% in the first
year and by 20% in the second year. If the population at the end of the second year is 39,600, find the population at the beginning of the first year.Solution
Let initial population = P. After first year (10% increase): = P × 110/100 = 11P/10 After second year (20% increase): = (11P/10) × 120/100 = 11P/10 × 6/5 = 66P/50 = 33P/25 Given 33P/25 = 39,600 ⇒ 33P = 39,600 × 25 39,600 × 25 = 39,600 × (100/4) = 3,960,000 / 4 = 990,000 So 33P = 990,000 P = 990,000 / 33 = 30,000
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