If $\frac{5}{x}+\frac{3}{y}=4$ and $\frac{3}{x}+\frac{5}{y}=2,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

Formulate the following problems as a pair of equations,and hence find their solutions:
Roohi travels $300 \ km$ to her home partly by train and partly by bus. She takes $4 \ hours$ if she travels $60 \ km$ by train and the remaining by bus. If she travels $100 \ km$ by train and the remaining by bus,she takes $10 \ minutes$ longer. Find the speed of the train and the bus separately.

$A$ 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 $km/h$).

Solve the following pair of equations by reducing them to a pair of linear equations:
$6x + 3y = 6xy$
$2x + 4y = 5xy$

Solve the following pair of linear equations using the cross-multiplication method:
$5x + 2y = 10$
$4x + 3y - 1 = 0$

In cyclic quadrilateral $ABCD$,$m \angle A = 2x + 4$,$m \angle B = y + 3$,$m \angle C = 2y + 10$,and $m \angle D = 4x - 5$. Find the measures of all four angles.