Two persons A and B are standing diametrically opposite on a circular track of with a radius of $3.5$ units. They start running in an opposite direction on the circular track and their speeds are four units/ min and seven units/min, respectively. On meeting each other, they take rest for half a min and then start running with twice the original speed. In five min, how many times will they take rest together?

Route-$1$ Travel by train from Chiplun to Mumbai and then from Mumbai to Pune. The trains take $4.5 \mathrm{h}$ and $3 \mathrm{h}$, respectively.

Route-$2$ Travel by a bus via Bhor. The distance covered by this route is $300 \mathrm{km}$ at $40 \mathrm{km}/\mathrm{h}$ and there is a half an hour break in between.

The numbers expressing (in meters) the length of fast and slow trains are three times the numbers expressing (in $\mathrm{km}/\mathrm{h}$) the speed of the slow and the fast train respectively. The speed of the slow train and that of the fast train consists of the same two digits, but in reverse order. The time taken by the two trains to pass each other, when travelling in an opposite direction on parallel lines will be:

Michael Johnson is a great sprinter. He can climb $12$stairs of a staircase in $3 \mathrm{s}$. But after climbing 480 stairs his speed reduces to eight stairs in $3 \mathrm{s}$. The Empire State Building in NY has $90$ floors and the lift takes $4 \mathrm{s}$ per floor. To get to the next floor, one has to climb $12$stairs. If Michael is on the ground floor how should he reach the ${90}^{\mathrm{th}}$ floor to be the first?