Starting from his house,a student walks at a speed of $2.5 \, km/hr$ and reaches his school $6 \, minutes$ late. Next day he increases his speed by $1 \, km/hr$ and reaches the school $6 \, minutes$ early. How far is the school from his house? (in $km$)

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 $km/h$)

$A$ train crosses a platform in $30 \, s$ travelling with a speed of $60 \, km/h$. If the length of the train is $200 \, m$, then the length of the platform is (in $m$):

$A$ is faster than $B$. $A$ and $B$ each walk $24 \, km$. The sum of their speeds is $7 \, km/hr$,and the sum of the time taken by them is $14 \, hours$. Then $A$'s speed is equal to (in $km/hr$)

In a race of $800\, m,$ $A$ can beat $B$ by $40\, m$. In a race of $500\, m,$ $B$ can beat $C$ by $5\, m$. In a race of $200\, m,$ $A$ will beat $C$ by? (in $m$)

$50$ trees are standing in a line such that the distance between any two consecutive trees is the same. $A$ car takes $18 \, seconds$ to travel from the $13^{th}$ tree to the $34^{th}$ tree. How much time (in $seconds$) will it take to reach from the first tree to the $50^{th}$ tree?