If a $110 \, m$ long train passes a man walking at a speed of $6 \, km/h$ against it in $6 \, s$,it will pass another man walking at the same speed in the same direction in how many seconds?

$A$ man walking at $3 \, km/h$ crosses a square field diagonally in $2 \, minutes$. The area of the field (in $m^2$) is:

Two cars $P$ and $Q$ start at the same time from $A$ and $B$ which are $120 \, km$ apart. If the two cars travel in opposite directions,they meet after $1 \, hour$,and if they travel in the same direction (from $A$ towards $B$),then $P$ meets $Q$ after $6 \, hours$. What is the speed of car $P$ (in $km/hr$)?

Two trains $A$ and $B$ start at the same time from Delhi and Patna respectively towards each other. They meet after $16 \, h$. If the distance between Delhi and Patna is $1872 \, km$ and train $B$ runs $27 \, km/h$ faster than train $A$,what is the speed of train $A$ in $km/h$?

Three men step off together from the same spot. Their steps measure $63 \, cm$,$70 \, cm$,and $77 \, cm$ respectively. The minimum distance each should cover so that all can cover the distance in complete steps is (in $cm$):

$A$ train,after travelling $50 \, km$,meets with an accident and then proceeds at $\frac{3}{4}$ of its former speed and arrives at its destination $35 \, minutes$ late. Had the accident occurred $72 \, km$ further,it would have reached the destination only $15 \, minutes$ late. The normal speed of the train (in $km/hr$) is: