$A$ train covers a distance of $10 \text{ km}$ in $12 \text{ minutes}$. If its speed is decreased by $5 \text{ km/hr}$,the time taken by it to cover the same distance will be:

$A$ person travels from $P$ to $Q$ at a speed of $40 \, km/h$ and returns from $Q$ to $P$ by increasing his speed by $50\%$. What is his average speed for the entire journey? (in $km/h$)

$A$ $180 \, m$ long train crosses another $270 \, m$ long train running from the opposite direction in $10.8 \, s$. If the speed of the first train is $60 \, km/h$,what is the speed of the second train in $km/h$?

Rakesh sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other,they complete their journeys in $9$ and $16 \, \text{hours}$,respectively. At what speed does Suresh cycle if Rakesh cycles at $16 \, \text{km/h}$?

Two trains start at the same time from Mumbai and Pune and proceed towards each other at the speeds of $60\, km/h$ and $40\, km/h$, respectively. When they meet, it is found that one train has travelled $20\, km$ more than the other. Find the distance between Mumbai and Pune (in $km$).

If the length of the train is $700 \, m$ and the length of the platform is $500 \, m$,find the time taken by the train moving at $54 \, km/h$ to cross the platform (in $sec$).