Population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that z is ...

Question

Population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that z is greater than y. Let P be the ratio of the population of state X to state Y in a given year. The percentage increase in P from 2001 to 2011 is ______.

A. (x - y)%
B. x%
C. y%
D. [(100 + x)/(100 + y) - 1] * 100%

Accepted Answer

[(100+x)/(100+y) - 1] * 100% (option D) If X's population is A in 2001, it becomes A*(1 + x/100) in 2011. If Y's population is B in 2001, it becomes B*(1 + y/100) in 2011. The ratio P in 2001 is A/B; in 2011 it is [A*(1+x/100)] / [B*(1+y/100)] = (A/B) * (1+x/100)/(1+y/100). The percentage increase in P is [(P_2011 - P_2001)/P_2001] * 100 = [(1+x/100)/(1+y/100) - 1] * 100 = [(100+x)/(100+y) - 1] * 100. Note: option A (x-y)% is only an approximation valid when x and y are small.