A train which moves with uniform speed for a certain distance takes $6 \mathrm{hours}$less if its speed is increased by $6 \mathrm{km} \mathrm{per} \mathrm{hour},$ it would have taken $6 \mathrm{hours}$ more, had its speed been decreased by $4 \mathrm{km} \mathrm{per} \mathrm{hour}.$ Find the distance of the journey and the speed of the train.

A man can row $8 \mathrm{km}/\mathrm{h}$​ in still water and he finds that it takes him twice as long to row up as to row down the stream. What is the rate of the stream.

A person $\mathrm{A}$ walks a certain distance. Had she walked half a km an hour faster than she did, she would have taken half an hour less, but had she walked half a km an hour slower, she would have taken $40 \mathrm{minutes}$ more. Find the distance and her rate of walking.

A wizard having powers of magical medicines seeing a cock fight going on, spoke privately to both the owners of cocks. To one he said, if your bird wins, then you give me your stake-money, but if you do not win, I shall give you two third of that. Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only $12$ gold pieces. Tell me $\mathrm{O}$ Ornament of the first rate Mathematicians, the stake of money each of the cock-owners.

Write the values of '$k$' for which the system of equations: $x+ky=0,$ $2x-y=0$ has a unique solution.