Find the time for which compound interest of $\text{Rs. }331$ was generated on a principal of $\text{Rs. }1,000$ at an annual interest rate of $10\%$.

We know the compound interest formula for total amount ($A$):
$$A=P{\left(1+\frac{R}{100}\right)}^n$$

Given:

* Principal ($P$) $=\text{Rs. }1,000$
* Compound Interest ($\text{CI}$) $=\text{Rs. }331$
* Total Amount ($A$) $=P+\text{CI}=1000+331=\text{Rs. }1331$
* Rate ($R$) $=10\%$

Substitute the values into the formula:

$$1331=1000{\left(1+\frac{10}{100}\right)}^n$$

$$\frac{1331}{1000}={\left(\frac{110}{100}\right)}^n$$

$$\frac{1331}{1000}={\left(\frac{11}{10}\right)}^n$$

We know that $1331=11^3$ and $1000=10^3$:

$${\left(\frac{11}{10}\right)}^3={\left(\frac{11}{10}\right)}^n⟹n=3\text{ years}$$