$A$ 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:

$A$ lent ₹ $5,000$ to $B$ for $2$ years and ₹ $3,000$ to $C$ for $4$ years on simple interest at the same rate of interest and received ₹ $2,200$ in all from both of them as interest. The rate of interest (in $\%$) per annum is:

Nitin borrowed some money at the rate of $6 \% \text{ p.a.}$ for the first three years,$9 \% \text{ p.a.}$ for the next five years,and $13 \% \text{ p.a.}$ for the period beyond eight years. If the total interest paid by him at the end of eleven years is ₹ $8,160$,the money borrowed by him was:

During the first year,the population of a village is increased by $5 \%$ and in the second year it is diminished by $5 \%$. At the end of the second year,its population was $47880$. What was the population at the beginning of the first year?

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 $Rs.$)?