Explanation:

To find out in how many years Rs8,000 becomes Rs12,167 at 15% per annum, compounded annually, we use the compound interest formula:

$$A=P(1+r/n{)}^{nt}$$

Where:

- $A$ is the final amount (Rs12,167)

- $P$ is the principal amount (Rs8,000)

- $r$ is the rate of interest (15% or 0.15)

- $n$ is the number of times interest is compounded per year (1 for annually)

- $t$ is the time in years

- Calculate $t$:

- Plug the values: $12,167=8,000(1+0.15{)}^t$

- Simplify to find $t$: $1.521=(1.15{)}^t$

- By trial, when $t=3$, $(1.15{)}^3=1.520875$ (approximately 1.521)

- Option:1, 3 years

- Option:2, 2 years

- Option:3, 5 years

- Option:4, 4 years