Question 146

The population of town B is 300%more than that of town A.For the next two years. the population ofA increases by x% per year and that of B decreases by the same percentage per year. After 2 years, if the population of A and B become equal, then the value of x is .........

Solution

Let the population of town A be a.

Population of town B = $$a + 300 \times \frac{300}{100} = 4a$$

After the next 2 year -

a $$\times (1+\frac{x}{100})^2 = 4a \times (1-\frac{x}{100})^2$$

$$(100+x)^2 = 4 \times (100 - x)^2$$

100 + x = 2(100 - x)

3x = 100

x = 33$$\frac{1}{3}$$

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