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

$A$ 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 $12 \% \text{ p.a.}$

If a certain sum of money borrowed at $5 \%$ per annum simple interest amounts to ₹ $1020$ in $4$ years,then the sum of money (in ₹) borrowed is:

$A$ sum of ₹ $26000$ was lent out in two parts in such a way that the interest on one part at $10 \%$ for $5$ $years$ is equal to that on the other part at $9 \%$ for $6$ $years.$ The sum lent out at $10 \%$ is (In ₹)

Arun gives his wife Asha a birthday gift,giving her each year a number of rupees equal to the number of years of her age. If her birthday falls on $August \, 8$,what sum must be placed at simple interest at $7 \%$ on $January \, 1$,before she is $42$,in order to raise the required sum (in $Rs.$)?

The simple interest on a sum of money is $\frac{4}{9}$ of the principal. Find the rate per cent and time,if both are numerically equal.