$A$ certain sum becomes $5$ times in $3$ years at simple interest. In how many years will it become $13$ times?

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?

$A$ 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:

The simple interest on a certain sum of money at the rate of $5 \%$ per annum for $8$ years is ₹ $840$. What is the rate of interest per annum for which the same amount of interest can be received on the same sum after $5$ years (in $\%$)?

Anil invested an amount for $3$ $years$ at a simple interest rate of $9$ $p.c.p.a.$ He got an amount of $Rs. 19050$ at the end of $3$ $years.$ What principal amount (in $Rs.$) did he invest?

If the simple interest on a certain sum of money after $6 \frac{1}{4}$ years is $\frac{3}{8}$ of the principal,then the rate of interest (in $\%$) per annum is