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

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?

$A$ 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 ₹)

Rakesh borrowed ₹ $5000$ from Ganesh at simple interest. If Ganesh received ₹ $500$ more than his capital after $5$ years,then the rate of interest (in $\%$) per annum is:

Deepak lent ₹ $8800$ to Jaichand for $13$ $years$ and ₹ $5500$ to another person for $12$ $years$ at the same rate of simple interest. He received ₹ $14432$ in total as interest from both. The rate of interest (in $\%$) per annum is:

$A$ certain sum becomes ₹ $1020$ in $5$ years and ₹ $1200$ in $8$ years at simple interest. What is the value of Principal (in ₹)?