correct answer is: a) 10 years and 5 months

Explanation

Let,
Principal = ‘p’
According to the question,
Interest will be \large\frac{5}{8} of itself.
So, Interest (S.I.) =\left(\frac{5}{8}\ \times\ p\right) or \large\frac{5p}{8}
Rate (r) = 6 %
Time = ‘t’
Now, S.I. =\large\frac{p\times r\times t}{100}
\rightarrow\large\frac{5p}{8}=\frac{p\times6\times t}{100}
\rightarrow\large\frac{5p}{8}=\frac{6pt}{100}
\rightarrow48pt=500p
\rightarrow t=\large\frac{500p}{48p}
\rightarrow t=\ 10.42
\therefore The time is 10.42 years or 10 years + \left(0.42\times12\right) months or 10 years 5.04 months.
Ans: The interest on a certain sum of money at 6% will be 5 by 8 of itself in 10 years and 5 months.

An alternative way to phrase this particular query is possible:
1. Calculate the total amount obtained from an investment of Rs 6500 at a simple quarterly interest rate of 8% over a period of 2 and a half years.
2. Find out the final value of an investment of Rs 6500 with a simple quarterly interest rate of 8% for 2 and a half years.
3. Determine the total sum accumulated from Rs 6500 invested at a simple quarterly interest rate of 8% for 2 and a half years.
4. What is the total amount obtained after investing Rs 6500 at a simple quarterly interest rate of 8% for 2 and a half years?
5. Calculate the final value of an investment of Rs 6500 with a simple quarterly interest rate of 8% over a period of 2 and a half years.