In what time will the simple interest be $2/5$ of the principal at $8\%$ per annum?

1. Let the Principal be $P$. According to the problem, the Simple Interest ($SI$) is:
$$SI=\frac{2}{5}P$$
The rate of interest is $R=8\%$.Use the standard Simple Interest formula:
$$SI=\frac{P\times R\times T}{100}$$
Substitute the given values into the formula:
$$\frac{2}{5}P=\frac{P\times 8\times T}{100}$$
Divide both sides by $P$ and solve for $T$:
$$\frac{2}{5}=\frac{8T}{100}$$
$$8T=\frac{2\times 100}{5}=40⟹T=\frac{40}{8}=5\text{ years}$$