$A$ passenger train $150 \ m$ long is travelling with a speed of $36 \ km/h$. If a man is cycling in the direction of the train at $9 \ km/h$,then the time taken by the train to pass the man is? (in $s$)

$A$ 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

$A$ car travels the first one-third of a certain distance with a speed of $10\, km/hr$,the next one-third distance with a speed of $20\, km/hr$,and the last one-third distance with a speed of $60\, km/hr$. The average speed of the car for the whole journey is (in $km/hr$):

Two trains of lengths $120 \,m$ and $80 \,m$ are running in the same direction with velocities of $40 \,km/h$ and $50 \,km/h$ respectively. The time taken by them to cross each other is (in $sec$).

An athlete runs a $200$ $\text{meters}$ race in $24$ $\text{seconds}$. His speed is (in $\text{km/hr}$):

$A$ dog finds a cat at $25$ leaps away. The cat sees the dog coming towards it and starts running with the dog in hot pursuit. In every minute, the dog makes $5$ leaps and the cat makes $6$ leaps, and one leap of the dog is equal to $2$ leaps of the cat. Find the time in which the dog will catch the cat (in minutes).