Single correct option
The population of a town increased by 10% in the first year, decreased by 10% in the second year and increased by 20% in the third year. If the population at the end of the third year was 1,18,800, what was the population at the beginning of the first year?
- A. 95,000
- B. 98,000
- C. 99,000
- D. 1,00,000
Show answer and solution
Answer: (D) 1,00,000
Net multiplier = 1.1 × 0.9 × 1.2 = 1.188.
Initial population = 1,18,800 ÷ 1.188 = 1,00,000.
Note that +10% followed by −10% is not zero change; it is a net 1% loss (1.1 × 0.9 = 0.99). So 1,18,800/1.2 = 99,000 is the population after year 2, and 99,000/0.99 = 1,00,000.
Tip: Successive percentage changes multiply; never add them.
Initial population = 1,18,800 ÷ 1.188 = 1,00,000.
Note that +10% followed by −10% is not zero change; it is a net 1% loss (1.1 × 0.9 = 0.99). So 1,18,800/1.2 = 99,000 is the population after year 2, and 99,000/0.99 = 1,00,000.
Tip: Successive percentage changes multiply; never add them.
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