At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

A train X departs from station A at 11.00 a.m. for station B, which is 180 km away.Another train Y departs from station B at 11.00 a.m. for station A. Train  X travels at an average speed of 70 kms/hr and does not stop anywhere until it arrives at station B.Train Y travels at an average speed of 50 kms/hr, but has to stop for 15 minutes at station C, which is 60 kms away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest km, from station A to the point where the trains cross each other?

Sum of lengths of two trains are given. Speed of the longer train is less than the speed of the smaller train and both the speeds are given. We can find out the time taken by these trains to cross each other while passing in the opposite direction.

State whether true or false.

Two runners A and B are running on a linear track. The length of the linear track is given. B gives a start of $10 \mathrm{s}$ to A and both of them finish the race in a dead heat. With the information given, we can find out the ratio of the speed of A and B.

State whether true or false.

There are five runners running on a circular track starting from the same point in the same direction same time. If we know the speeds of each of the runners and the distances between each of the possible distinct meeting points between any two of them is given, we can find out the length of track.

State whether true or false.

Two towns $\mathrm{A}$ and $\mathrm{B}$ are $60 km$ apart. A school is to be built to serve $150$ students in town$A$ and $50$ students in town $B$. If the total distance to be travelled by all $200$ students is to be as small as possible, then the school should be built at :