a) 10%

b) 8%

c) 6%

d) 12 ½%

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?**