Explanation

Here sum means Principal.
Time =2\frac{1}{2} years or \frac{5}{2} years
Let,
Rate = ‘r’ %
Principal =₹ x
\therefore Amounts =\left(x\times\frac{6}{5}\right) or ₹\frac{6x}5
\therefore S.I. =\left(amount\ -\ principle\right)
\rightarrow S.I. =\left(\frac{6x}{5}-x\right)
\rightarrow S.I. =\left(\frac{6x-5x}{5}\right) _[L.C.M=5]
\rightarrow S.I. =\frac{x}{5}
We know, S.I. =\frac{P\times R\times T}{100}
According to the question,
\frac{x}{5}=\frac{x\times r\times5}{100\times2}
\rightarrow\frac{x}{5}=\frac{5rx}{200}
\rightarrow25rx=200x
\rightarrow r=\frac{200x}{25x}
\rightarrow r=8 %
\therefore The rate of interest per annum is 8 %
Ans: 8 %.

This particular question can also be asked in the following way:
1. What is the rate of interest per annum if a sum becomes 6/5 of itself in 2 ½ years at simple interest?
2. How to calculate the rate of interest per annum when a sum grows to 6/5 of its initial value in 2 ½ years with simple interest?
3. Explain the method to find the rate of interest per annum when a principal amount increases to 6/5 of its value in 2 ½ years under simple interest.
4. In simple interest, if a sum becomes 6/5 of itself in 2 ½ years, what is the annual rate of interest?
5. Calculate the annual rate of interest in a simple interest scenario where a sum becomes 6/5 of itself in 2 ½ years.