A sum of money becomes 8/5 of itself in 5 years at a certain rate of interest. What is the rate of the interest?

Let the sum of money be P(which is the principal value) and rate of interest be R.
According to the question,
Amount (principal +simple interest) = 8P/5
Time (T) = 5 years
Simple interest (SI) = PRT/100
SI = 5PR/100
Amount = P + SI
8P/5 = P + (5PR/100)
8P/5 = P(100 + 5R)/100
160 = 100 + 5R
5R = 60
R = 12
Therefore, rate of interest = 12% p.a.

Alternative Method:
Given A = 8/5p (8/5 of the sum) .
Time = 5years .
Let the sum be P = 100.
Then, the amount = 8/5p = (value of p is 100)
= 8/5 × 100
= 160 .
S. I. = A-P
= 160 - 100
= 60 .
Hence,
Rate = S.I. × 100/P × T
= 60 × 100/100 × 5
= 12% p.a.