If $y = \frac{1}{2} x$ and $x + 2y = 8$,then $x = \dots$

Solve the following pairs of equations by the method of elimination:
$5x - 3y = 1$
$2x + 5y = 19$

$A$ motor boat can travel $30 \, km$ upstream and $28 \, km$ downstream in $7 \, hours$. It can travel $21 \, km$ upstream and return in $5 \, hours$. Find the speed of the boat in still water and the speed of the stream (in $km/h$).

$x$ years ago,the age of Mahesh was $y$ years. Then,after $z$ years,his age will be $\ldots$ years.

$A$ two-digit number is obtained by either multiplying the sum of the digits by $8$ and then subtracting $5$,or by multiplying the difference of the digits by $16$ and then adding $3$. Find the number.

Aruna has only $Rs. 1$ and $Rs. 2$ coins with her. If the total number of coins that she has is $50$ and the amount of money with her is $Rs. 75$,then the number of $Rs. 1$ and $Rs. 2$ coins are,respectively