16. In a particular fraction the numerator and denominator are both positive. The numerator of this fraction is increased by $40 \%$. By what percentage should its denominator be decreased so that the new fraction is double the original fraction?
A $10 \%$
B $20 \%$
C $30 \%$
D $40 \%$
E $50 \%$
SolUTION
C

Let the original fraction be $\frac{x}{y}$. Since the numerator of the new fraction is obtained by increasing the numerator of the old fraction by $40 \%$, its value is $1.4 x$. Let the denominator of the new fraction be $k y$. We are told that the new fraction is twice the old fraction and hence $\frac{1.4 x}{k y}=2\left(\frac{x}{y}\right)$. Therefore $\frac{1.4}{k}=2$ and hence $k=0.7$. Therefore the denominator of the new fraction is $70 \%$ of the denominator of the original fraction and hence has been decreased by $30 \%$.