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