Discussion

Explanation:

Every month the population increased by x% and then decreased by y%.

∴ overall % change every month = x - y + (x × -y)/100 %
Let this be p%

Now, if p > 0, then the population every month should increase and the population at the end of the year should be more than the starting population. Hence, p cannot be greater than 0.

Now, if p < 0, then the population every month should decrease and the population at the end of the year should be less than the starting population. Hence, p cannot be less than 0.

∴ p = 0%

⇒ x - y + (x × -y)/100 = 0

⇒ x - xy/100 = y

⇒ x(100 - y)/100 = y

⇒ x = $\frac{100}{100-y}\times y$

Now, y < 100 (the population cannot decrease by 100%)
∴ $\frac{100}{100-\mathrm{y}}>1$

⇒ x = $\frac{100}{100-y}\times y$ > y

Hence, option (b).

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