Solve the following pairs of equations by the cross-multiplication method:
$4x + 6y = 11$
$5x - 8y = 6$

$A$ train covered a certain distance at a uniform speed. If the train would have been $10\, km/h$ faster,it would have taken $2\, hours$ less than the scheduled time. And,if the train were slower by $10\, km/h$,it would have taken $3\, hours$ more than the scheduled time. Find the distance covered by the train. (in $, km$)

Naresh has double the money that Yogesh has. If Naresh gives Yogesh ₹ $20$,then both have equal money. The pair of equations obtained from this data is $\ldots \ldots \ldots \ldots .$

If $\frac{x+y}{x y}=2$ and $\frac{x-y}{x y}=6,$ then $x=\ldots \ldots \ldots \ldots .$

The sum of the digits of a two-digit number is $6$. The number obtained by interchanging the digits is $18$ less than the original number. Find the original number.

Five years ago,the sum of the ages of five persons was $50$ years. After five years,the sum of the ages of those five persons will be $\ldots \ldots \ldots \ldots$ years.