If a principal becomes twice of its amount in $10$ years, the rate of simple interest per annum is:

Note: The phrase "becomes twice of its amount" traditionally means that the final amount ($A$) is twice the principal ($P$).
Therefore, $A=2P$.

$$\text{Simple Interest }(\text{SI})=A-P=2P-P=P$$

$$\text{Time }(T)=10\text{ years}$$

Using the formula $\text{SI}=\frac{P\times R\times T}{100}$:

$$P=\frac{P\times R\times 10}{100}$$

$$1=\frac{R}{10}⟹R=10\%\text{ per annum}$$