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 $9975$ at the end of the second year, then what was the population size in the beginning of the first year?

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Solution

Let the population of a town is $100$
Then $5 %$ increased population after first year $= 100 + 5 = 105$
So, $5 %$ decreased population after second year $= 105 - (\frac{5}{100} \times 105) = 105 - 5.25 = 99.75$
But, the population after second year is $9975$
Then, the population at the beginning of the year is
$\frac{100}{99.75} \times 9975 = 10000$

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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 9975 at the end of the second year, then what was the population size in the beginning of the first year?

Let the population of a town is 100Then 5% increased population after first year =100+5=105So, 5% decreased population after second year =105−(5100×105)=105−5.25=99.75But, the population after second year is 9975Then, the population at the beginning of the year is10099.75×9975=10000

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 $9975$ at the end of the second year, then what was the population size in the beginning of the first year?