Jyrki's answer is correct. First, take the percentage, rewrite it as a decimal, and add 1 to it. So if the tax increases the price by 5% for example, we multiply the price by 1.05. If the other tax is 10% (and this is a strange tax that taxes tax...), we multiply it again by 1.1. So if the original price is $a$, our new cost is
$1.1(1.05a)=(1.1\times1.05)a=1.155a$
Now, to get the percent increase, we just subtract out 1 again and write it as a percent. The increase in cost is $.155a$, so a 5% tax and 10% tax will increase the cost by 15.5%