15. The Grand Old Duke of York had 10000 men. He lost $10 \%$ of them on the way to the top of the hill, and he lost $15 \%$ of the rest as he marched them back down the hill. What percentage of the 10000 men were still there when they reached the bottom of the hill?
A $76 \frac{1}{2} \%$
B $75 \%$
C $73 \frac{1}{2} \%$
D $\quad 66 \frac{2}{3} \%$
E $25 \%$
Solution: $\mathbf{A}$
After losing $10 \%$ of the men, the Grand Old Duke of York was left with $90 \%$ of them. After losing $15 \%$ of these, he was left with $85 \%$ of the remaining $90 \%$ men. So he is left with $\frac{85}{100} \times \frac{90}{100}$ $=\frac{7650}{10000}=\frac{76.5}{100}$ of the men he started, that is, $76 \frac{1}{2} \%$ of the original number of men.