In a rectangle,the length is $3$ less than twice its width. The perimeter of the rectangle is $100$. Represent this situation as a pair of linear equations in two variables.

$A$ shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days,and an additional charge for each day thereafter. Latika paid $Rs. 22$ for a book kept for six days,while Anand paid $Rs. 16$ for the book kept for four days. Find the fixed charges and the charge for each extra day (in $Rs.$).

If the following pair of equations is consistent (unique solution),then find the value of $k$:
$x - ky = 2$
$3x + 2y = -5$

For which values of $a$ and $b$ does the following pair of linear equations have an infinite number of solutions?
$2x + 3y = 7$
$(a-b)x + (a+b)y = 3a + b - 2$

Find the value$(s)$ of $p$ for the pair of equations $2x + 3y - 5 = 0$ and $px - 6y - 8 = 0$ if the system has a unique solution.

Susan invested a certain amount of money in two schemes $A$ and $B,$ which offer interest at the rate of $8 \%$ per annum and $9 \%$ per annum,respectively. She received $Rs.\, 1860$ as annual interest. However,had she interchanged the amount of investments in the two schemes,she would have received $Rs.\, 20$ more as annual interest. How much money did she invest in each scheme?