Last year Mr. Jon Q. Public received an inheritance. He paid $20\%$ in federal taxes on the inheritance, and paid $10\%$ of what he had left in state taxes. He paid a total of $\textdollar10500$ for both taxes. How many dollars was his inheritance?
$(\mathrm {A})\ 30000 \qquad (\mathrm {B})\ 32500 \qquad(\mathrm {C})\ 35000 \qquad(\mathrm {D})\ 37500 \qquad(\mathrm {E})\ 40000$
After paying his taxes, he has $0.8*0.9=0.72$ of his earnings left. Since $10500$ is $0.28$ of his income, he got a total of $\frac{10500}{0.28}=37500\  \mathrm{(D)}$.