$A$ 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 $\%$):

Mayuri took a loan at a simple interest rate of $6 \, p.c.p.a.$ in the first year,and the rate increased by $1.5 \, p.c.p.a.$ every year. If she paid $Rs. 8190$ as interest at the end of $3 \, years$,what was her loan amount (in $Rs.$)?

The population of a town is $11200$. It increases by $25\%$ in the first year and decreases by $15\%$ in the second year. What is the population of the town at the end of $2$ years?

If ₹ $1000$ is invested at an interest rate of $5 \%$ and the interest is added to the principal every $10$ years,then the number of years in which it will amount to ₹ $2000$ is:

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 $Rs.$)?

$A$ man invests ₹ $3965$ in the names of his three daughters,Neeta,Sita,and Gita,in such a way that they would receive the same amount after $2, 3,$ and $4$ years. If the rate of interest is $5 \%$ p.a.,then the amount (in ₹) invested for Neeta,Sita,and Gita is: