If a train $110 \, m$ long passes a telegraph pole in $3 \, seconds$,then the time taken (in $seconds$) by it to cross a railway platform $165 \, m$ long is:

By walking at $\frac{3}{4}$ of his usual speed,a man reaches his office $20 \text{ minutes}$ later than usual. His usual time is (in $\text{minutes}$):

$A$ 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 $AM$):

One aeroplane started $30 \, \text{minutes}$ later than the scheduled time from a place $1500 \, \text{km}$ away from its destination. To reach the destination at the scheduled time,the pilot had to increase the speed by $250 \, \text{km/hr}$. What was the original speed of the aeroplane? (in $\text{km/hr}$)

$A$ man travelled a distance of $80 \, km$ in $7 \, h$,partly on foot at the rate of $8 \, km/h$ and partly by bicycle at $16 \, km/h$. The distance travelled on foot is (in $km$):

$A$ train completes a non-stop journey in $8 \, \text{hours}$. If it had travelled $5 \, \text{km/h}$ faster, it would have completed the journey in $6 \, \text{hours} \, 40 \, \text{minutes}$. What is its lowest speed in $\text{km/h}$?