A shopkeeper allows a discount of $10\%$ on an item. How much per cent above the cost price should he mark his goods to make a profit of $10\%$?

Let the Cost Price (CP) of the goods be $100$.To make a profit of $10\%$, the Selling Price (SP) must be:
$$\text{SP}=100+10=110$$
A discount of $10\%$ is given on the Marked Price (MP):
$$\text{SP}=\text{MP}\times \left(1-\frac{10}{100}\right)=\text{MP}\times \frac{90}{100}$$
$$110=\text{MP}\times \frac{9}{10}$$
$$\text{MP}=\frac{1100}{9}=122\frac{2}{9}$$
Markup percentage above Cost Price:
$$\text{Markup}\%=\text{MP}-\text{CP}=122\frac{2}{9}-100=22\frac{2}{9}\%$$