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

The sum of the digits of a two-digit number is $9$. If $27$ is added to it,the digits of the number get reversed. The number is

$A$ two-digit number is obtained by either multiplying the sum of the digits by $8$ and adding $1$,or by multiplying the difference of the digits by $13$ and adding $2$. Find the number.

Is it true to say that the pair of equations $-x + 2y + 2 = 0$ and $\frac{1}{2}x - \frac{1}{4}y - 1 = 0$ has a unique solution? Justify your answer.

Devarshi got thrice the marks as obtained by Maharshi in the annual examination of mathematics of standard $10$. The sum of the marks obtained by them was $150$. Represent this situation as a pair of linear equations in two variables.

If $2x + y = 23$ and $4x - y = 19$,find the values of $5y - 2x$ and $\frac{y}{x} - 2$.