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 $Rs.$)?

Sapna borrowed a certain sum of money from Kavita under the following repayment scheme based on simple interest: $8 \%$ $p.a.$ for the initial $2$ $years$,$9.5 \%$ $p.a.$ for the next $4$ $years$,$11 \%$ $p.a.$ for the next $2$ $years$,and $12 \%$ $p.a.$ after the first $8$ $years$. Find the total amount (in $Rs.$) which a sum of $Rs. 9000$ taken for $12$ $years$ becomes at the end of $12$ $years$.

The rate of interest on a sum of money is $4 \%$ per annum for the first $2$ years,$6 \%$ p.a. for the next $4$ years,and $8 \%$ p.a. for the period beyond $6$ years. If the simple interest accrued by the sum for a total period of $9$ years is ₹ $1120$,then the sum (in ₹) is:

The simple interest on a sum of money is $\frac{8}{25}$ of the sum. If the number of years is numerically half the rate percent per annum,then the rate percent per annum is

If the simple interest on a certain sum of money is $\frac{4}{25}$ of the sum and the rate per cent equals the number of years,then the rate of interest (in $\%$) per annum is

$A$ lent ₹ $6000$ to $B$ for $2$ $years$ and ₹ $1500$ to $C$ for $4$ $years$ and received altogether from both ₹ $900$ as simple interest. The rate of interest is (in $\%$):