correct answer is: b) 8%

Explanation

Actually here ‘Sum’ indicates ‘Principal’
Let, Sum = ₹ 'x'
Rate = ‘r’ % p.a.
Time = 5 years
Simple Interest =₹\left(x\times\frac25\right) or ₹\frac{2x}5
We know, S.I. =\frac{p\times t\times r}{100}
According to the question,
\frac{2x}{5}=\frac{x\times5\times r}{100}
\rightarrow\ \frac{2x}{5}=\frac{5xr}{100}
\rightarrow25xr=200x _{[cross multiply]}
\rightarrow r=\frac{200x}{25x}
\rightarrow r=8 %
\therefore The rate percent per annum is 8 %
Ans: The rate percent per annum is 8 %.

An additional variation of this particular query is:
1) Calculate the annual interest rate if the simple interest on a sum for 5 years is 2/5 of the principal amount.
2) What is the rate percent per annum for simple interest if it amounts to 2/5 of the principal sum over a 5-year period?
3) Find the annual interest rate when the simple interest for 5 years is 2/5 of the original sum.
4) Determine the percentage rate per annum for simple interest when it equals 2/5 of the principal amount over a 5-year term.
5) In a scenario where the simple interest over 5 years is 2/5 of the sum, what is the annual rate of interest?