A merchant purchases $11$ toys for Rs. $10$ and sells $10$ toys for Rs. $11$. His profit percentage is:

To compare cost and sales easily, let us consider a common multiple number of toys. Take $\text{LCM}(11,10)=110$ toys.
Cost Price ($\text{CP}$) of $11$ toys = Rs. $10$

$$\text{CP of 110 toys}=\frac{10}{11}\times 110=\text{Rs. }100$$

Selling Price ($\text{SP}$) of $10$ toys = Rs. $11$

$$\text{SP of 110 toys}=\frac{11}{10}\times 110=\text{Rs. }121$$

Profit calculation:

$$\text{Profit}=\text{SP}-\text{CP}=121-100=\text{Rs. }21$$

$$\text{Profit }\%=\left(\frac{\text{Profit}}{\text{CP}}\times 100\right)\%=\left(\frac{21}{100}\times 100\right)\%=21\%$$