Solve the following pair of equations by the method of elimination:
$11x + 13y = 61$
$13x + 11y = 59$

$A$ boat goes $32 \, km$ upstream and $36 \, km$ downstream in $7$ hours. In $9$ hours,it can go $40 \, km$ upstream and $48 \, km$ downstream. Determine the speed of the stream and that of the boat in still water. (Speed of boat in still water is more than the speed of the stream of river.)

$A$ fraction becomes $\frac{1}{4}$ if $2$ is subtracted from the numerator and $3$ is added to the denominator. If $6$ is added to the numerator and the denominator is multiplied by $3$,it becomes $\frac{2}{3}$. Find the fraction.

The length of a rectangle is $5$ less than twice its breadth. If its perimeter is $110,$ find the area of the rectangle. Use the cross-multiplication method for the solution.

For what value$(s)$ of $k$ does the pair of equations $kx + 3y = k - 3$ and $12x + ky = k$ have no solution?

For a two-digit number,if the sum of its digits is equal to the product of its digits,then the number is .............