correct answer is: a) 1 year 3 months

Explanation

Here,
Principal (p) = ₹ 5000
Amount = ₹ 5500
S.I. = (Amount – Principal)
Or, S.I. =₹\left(5500-5000\right) or ₹ 500
Rate (r) = 8 % p.a.
Let, Time = ‘t’ years
We know, S.I. =\frac{p\ \times\ t\ \times\ r}{100}
\rightarrow500=\frac{5000\times t\times8}{100}
\rightarrow40000t=50000 _{[cross multiply]}
\rightarrow t=\frac{50000}{40000}
\rightarrow t=1.25
\therefore The time is 1.25 years or 1 years 3 months.
Ans: The time it would take for 5000 to become 5500 at an interest rate of 8% per annum is 1 year and 3 months.

Another way to phrase this particular query is:
1. Determine the duration required for an amount of Rs 5000 to grow to Rs 5500 at an annual interest rate of 8%.
2. Calculate the time it takes for Rs 5000 to reach Rs 5500 at an interest rate of 8% per annum.
3. Find out in how many years Rs 5000 will become Rs 5500 with an 8% per annum interest rate.
4. Calculate the time it takes for an investment of Rs 5000 to grow to Rs 5500 with an annual interest rate of 8%.
5. What is the period needed for Rs 5000 to accumulate to Rs 5500 at a rate of 8% per annum?