In what time will ₹ $8100$ produce the same income at $3 \%$ as ₹ $225$ in $4$ years at $3 \%$?

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 $Rs.$)?

Nutan borrowed some money at a rate of $4$ $p.c.p.a.$ for the first $3$ years,at the rate of $8$ $p.c.p.a.$ for the next $2$ years,and at the rate of $9$ $p.c.p.a.$ for the period beyond $5$ years. If she paid a total $SI$ of $Rs. 19550$ at the end of $7$ years,how much money (in $Rs.$) did she borrow?

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:

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

$A$ sum of $Rs. 725$ is lent in the beginning of a year at a certain rate of interest. After $8$ months,a sum of $Rs. 362.50$ more is lent but at the rate twice the former. At the end of the year,$Rs. 33.50$ is earned as interest from both the loans. What was the original rate (in $\%$) of interest?