If the following pair of equations is consistent (unique solution),then find the value of $k$:
$x - ky = 2$
$3x + 2y = -5$

Prashant purchases $2$ mobiles and $3$ memory cards for Rs. $6500$. The cost of one mobile and one memory card is Rs. $2950$. Represent this as a pair of linear equations in two variables.

The solution of the pair of equations $x+y-1=0$ and $2x+2y-3=0$ is:

Two years ago,the sum of the ages of a mother,father,and two daughters was $40$ years. After three years,what will be the sum of their ages?

It can take $12$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for $4$ hours and the pipe of smaller diameter for $9$ hours,only half the pool can be filled. How long would it take for each pipe to fill the pool separately?

$8$ men and $12$ women can finish a piece of work in $10$ days. While $6$ men and $8$ women can finish it in $14$ days. Find the time taken by one man alone and that by one woman alone to finish the work.