Question

Population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that x 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. $\frac{x}{y}$
• B. $\frac{100(x-y)}{100+y}$
• C. $x-y$
• D. $\frac{100(x-y)}{100+x}$

Answer 1

The correct option is B $\frac{100(x-y)}{100+y}$

$Leta,bbeinitialpopulation$

$Given\frac{a}{b}=p\left(ratioearlier\right)$

$\frac{a(1+\frac{x}{100})}{b(1+\frac{y}{100})}=p^{\prime }\left(newratio\right)$

$So,required\%change$


$\frac{p^{\prime }-p}{p}\times 100=\left[\frac{\frac{a}{b}\left(\frac{100+x}{100+y}\right)-\frac{a}{b}}{\frac{a}{b}}\right]\times 100$

$=\frac{100(x-y)}{100+y}$