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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