$A$ policeman starts to chase a thief. When the thief goes $10 \, \text{steps}$, the policeman moves $8 \, \text{steps}$. $5 \, \text{steps}$ of the policeman are equal to $7 \, \text{steps}$ of the thief. The ratio of the speeds of the policeman and the thief is

$A$ train leaves station $A$ at $5\, AM$ and reaches station $B$ at $9\, AM$ on the same day. Another train leaves station $B$ at $7\, AM$ and reaches station $A$ at $10.30\, AM$ on the same day. The time at which the two trains cross one another is (in $AM$):

$A, B$ and $C$ start at the same time in the same direction to run around a circular stadium. $A$ completes a round in $252 \text{ seconds}$,$B$ in $308 \text{ seconds}$ and $C$ in $198 \text{ seconds}$,all starting at the same point. After what time will they next meet at the starting point again?

$A$ bus takes $15\, hours$ to travel from Delhi to Chandigarh. The bus travels for one-third of the total time at a speed of $80\, km/h$. It travels for $40\%$ of the remaining time at a speed of $70\, km/h$. It travels for $\frac{2}{3}$ of the remaining time at a speed of $85\, km/h$,and the rest of the time at a speed of $100\, km/h$. What is the total distance covered by the bus?

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 $km$):

$A$ boy walking at a speed of $10\, km/hr$ reaches his school $15\, minutes$ late. Next time he increases his speed by $2\, km/hr$, but still he is late by $5\, minutes$. Find the distance of his school from his house (in $km$).