A sum amounts to Rs. $1180$ in $3$ years and to Rs. $1300$ in $5$ years. Find the rate of interest.

Let the principal be $P$ and the annual simple interest be $I$.
Amount in $5$ years: $P+5I=1300$
Amount in $3$ years: $P+3I=1180$

Subtracting the two equations:

$$(P+5I)-(P+3I)=1300-1180$$

$$2I=120⟹I=\text{Rs. }60\text{ (Interest per year)}$$

Now, find the principal $P$:

$$P+3I=1180⟹P+3(60)=1180⟹P+180=1180⟹P=\text{Rs. }1000$$

The rate of interest $R$ is:

$$R=\left(\frac{I}{P}\right)\times 100\%=\left(\frac{60}{1000}\right)\times 100\%=6\%\text{ per annum}$$