Shruti borrowed $Rs. 2500$ from her two friends. For one loan she paid $8 \%$ $p.a.$ and for the other $6 \%$ $p.a.$ simple interest. If she paid $Rs. 180$ as total interest for one year,how much did she borrow (in $Rs.$) at $8 \%$ $p.a.?$

$A$ 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?

For what sum (in ₹) will the simple interest at $R \%$ per annum for $2$ years be $R$?

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 $Rs.$)?

$A$ lends ₹ $2500$ to $B$ and a certain sum to $C$ at the same time at $7 \%$ $p.a.$ simple interest. If after $4$ $years,$ $A$ altogether receives ₹ $1120$ as interest from $B$ and $C,$ then the sum lent (in ₹) to $C$ is

According to a census report,the population growth rate of Faridabad is going to be an increasing $A.P.$ with the first year's rate as $5 \%$ and common difference as $5 \%$,but simultaneously the migration rate is an increasing $G.P.$ with the first term as $1 \%$ and common ratio of $2$. If the population on $31 \, \text{December}, 2010$ is $1 \, \text{million}$,then find in which year will Faridabad witness its first fall in population?