Discussion
During one year, the population of a town increased by 5% and during the next year, the population decreased by 5%. If the total population is 9,975 at the end of the second year, then what was the population size in the beginning of the first year?
Answer: D
A rise of 5% and then a fall of 5% leaves the population at 1.05 x 0.95 = 0.9975 of the start. So the start is 9975 / 0.9975 = 10,000, option D.
9,975 is the final figure itself, and 9,500 and 10,500 do not give 9,975 after the two changes.
Checking the answer: 10,000 increased by 5 per cent is 10,500, and a fall of 5 per cent on 10,500 is 525, which leaves 9,975, exactly the figure in the question. The common error is to think that a rise and a fall of the same percentage cancel out, which would give 9,975 as the start.
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