The population of town B is 300%more than that of town A.For the next two years. the population of A 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 _____.
Answer & explanation
Correct answer: option 2
Let the population of town A be 100
The population of B = 100 + 100 × \(\frac{300}{100}\) = 400
According to the question
100 × \(\frac{100+x}{100}\) × \(\frac{100+x}{100}\) = 400 ×\(\frac{100+x}{100}\) × \(\frac{100+x}{100}\)
(100 + x)2 = 4 (100 – x)2
\(\frac{(100+x)^2)}{(100-x)^2}\) = 4
\(\frac{100+x}{100-x}\) = \(\frac{2}{1}\)
Using dividendo and componendo,
\(\frac{100}{x}\) =\(\frac{2+1}{2-1}\)
\(\frac{100}{x}\) = \(\frac{3}{1}\)
x = \(\frac{100}{3}\)
= 33\(\frac{1}{3}\)%