Two trains of equal length are running on parallel tracks in the same direction at the speeds of $46 \, km/h$ and $36 \, km/h$. The faster train passes the slower train in $36 \, seconds$. The length of each train is (in $m$):

In a race of $1 \, km$,$A$ gives $B$ a start of $100 \, m$ and still wins by $20 \, s$. But if $A$ gives $B$ a start of $25 \, s$,$B$ wins by $50 \, m$. The time taken by $A$ to run $1 \, km$ is (in $s$):

Aditya is travelling on his cycle and has calculated that he will reach point $A$ at $2\, pm$, if he travels at $10\, km/h$. He will reach there at $12\, noon$, if he travels at $15\, km/h$. At what speed must he travel to reach $A$ at $1\, pm$? (in $km/h$)

$A$ boy started from his house by bicycle at $10:00 \, am$ at a speed of $12 \, km/h$. His elder brother started after $1 \, hour \, 15 \, minutes$ by scooter along the same path and caught him at $1:30 \, pm$. The speed of the scooter was (in $km/h$):

If $A$ travels to his school from his house at the speed of $3 \, km/h$,he reaches the school $5 \, minutes$ late. If he travels at the speed of $4 \, km/h$,he reaches the school $5 \, minutes$ earlier than the scheduled time. The distance of his school from his house is (in $km$):

$A$ man starts from his home and walks $10 \, km$ towards South. Then he turns right and walks $6 \, km$,again he turns right and goes $10 \, km$. Finally,he turns right and walks $5 \, km$. At what distance is he from his starting point? (in $km$)