Alipta received some amount of money from her father. In how many $years$ will the ratio of the money (principal) and the interest obtained from it be $10: 3$ at the rate of $6 \%$ simple interest per annum?

The simple interest on a certain sum of money at the rate of $5 \%$ per annum for $8$ years is ₹ $840$. What is the rate of interest per annum for which the same amount of interest can be received on the same sum after $5$ years (in $\%$)?

In how many years will ₹ $150$ produce the same interest at $8 \%$ per annum as ₹ $800$ produces in $3$ years at $4 \frac{1}{2} \%$ per annum?

At what rate per cent per annum will the simple interest on a sum of money be $\frac{2}{5}$ of the principal in $10$ $years$?

In how many years will a sum of money treble itself at $10 \%$ per annum simple interest?

$A$ sum of $Rs. 2540$ is lent out in two parts,one at $12 \%$ and the other at $12.5 \%$. If the total annual return on the total money invested is $Rs. 312.42$,find the money (in $Rs.$) lent at $12 \% \text{ p.a.}$